An Explicit Nonlinear Mapping for Manifold Learning.
Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo
2013-02-01
Manifold learning is a hot research topic in the held of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the hrst time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.
An Explicit Nonlinear Mapping for Manifold Learning
Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo
2010-01-01
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have...
Unraveling flow patterns through nonlinear manifold learning.
Tauro, Flavia; Grimaldi, Salvatore; Porfiri, Maurizio
2014-01-01
From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap) to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Unraveling flow patterns through nonlinear manifold learning.
Directory of Open Access Journals (Sweden)
Flavia Tauro
Full Text Available From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Adaptive sampling for nonlinear dimensionality reduction based on manifold learning
DEFF Research Database (Denmark)
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2017-01-01
We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...... that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric...... to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime....
Nonlinear manifold representations for functional data
Chen, Dong; Müller, Hans-Georg
2012-01-01
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which...
Manifold learning for object tracking with multiple nonlinear models.
Nascimento, Jacinto C; Silva, Jorge G; Marques, Jorge S; Lemos, Joao M
2014-04-01
This paper presents a novel manifold learning algorithm for high-dimensional data sets. The scope of the application focuses on the problem of motion tracking in video sequences. The framework presented is twofold. First, it is assumed that the samples are time ordered, providing valuable information that is not presented in the current methodologies. Second, the manifold topology comprises multiple charts, which contrasts to the most current methods that assume one single chart, being overly restrictive. The proposed algorithm, Gaussian process multiple local models (GP-MLM), can deal with arbitrary manifold topology by decomposing the manifold into multiple local models that are probabilistic combined using Gaussian process regression. In addition, the paper presents a multiple filter architecture where standard filtering techniques are integrated within the GP-MLM. The proposed approach exhibits comparable performance of state-of-the-art trackers, namely multiple model data association and deep belief networks, and compares favorably with Gaussian process latent variable models. Extensive experiments are presented using real video data, including a publicly available database of lip sequences and left ventricle ultrasound images, in which the GP-MLM achieves state of the art results.
Nonlinear manifold representations for functional data
Chen, Dong; 10.1214/11-AOS936
2012-01-01
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which we modify to address functional data settings. In simulations and applications, we study examples of functional data which lie on a manifold and validate the superior behavior of manifold mean and functional manifold components over traditional cross-sectional mean and functional principal components. We also include consistency proofs for our estimators under certain assumptions.
Butail, Sachit; Bollt, Erik M; Porfiri, Maurizio
2013-11-07
In this paper, we build a framework for the analysis and classification of collective behavior using methods from generative modeling and nonlinear manifold learning. We represent an animal group with a set of finite-sized particles and vary known features of the group structure and motion via a class of generative models to position each particle on a two-dimensional plane. Particle positions are then mapped onto training images that are processed to emphasize the features of interest and match attainable far-field videos of real animal groups. The training images serve as templates of recognizable patterns of collective behavior and are compactly represented in a low-dimensional space called embedding manifold. Two mappings from the manifold are derived: the manifold-to-image mapping serves to reconstruct new and unseen images of the group and the manifold-to-feature mapping allows frame-by-frame classification of raw video. We validate the combined framework on datasets of growing level of complexity. Specifically, we classify artificial images from the generative model, interacting self-propelled particle model, and raw overhead videos of schooling fish obtained from the literature. © 2013 Elsevier Ltd. All rights reserved.
Hashing on nonlinear manifolds.
Shen, Fumin; Shen, Chunhua; Shi, Qinfeng; van den Hengel, Anton; Tang, Zhenmin; Shen, Heng Tao
2015-06-01
Learning-based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes preserving the Euclidean similarity in the original space. Manifold learning techniques, in contrast, are better able to model the intrinsic structure embedded in the original high-dimensional data. The complexities of these models, and the problems with out-of-sample data, have previously rendered them unsuitable for application to large-scale embedding, however. In this paper, how to learn compact binary embeddings on their intrinsic manifolds is considered. In order to address the above-mentioned difficulties, an efficient, inductive solution to the out-of-sample data problem, and a process by which nonparametric manifold learning may be used as the basis of a hashing method are proposed. The proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available. It is particularly shown that hashing on the basis of t-distributed stochastic neighbor embedding outperforms state-of-the-art hashing methods on large-scale benchmark data sets, and is very effective for image classification with very short code lengths. It is shown that the proposed framework can be further improved, for example, by minimizing the quantization error with learned orthogonal rotations without much computation overhead. In addition, a supervised inductive manifold hashing framework is developed by incorporating the label information, which is shown to greatly advance the semantic retrieval performance.
Directory of Open Access Journals (Sweden)
Lin Liang
2015-01-01
Full Text Available A new method for extracting the low-dimensional feature automatically with self-organization mapping manifold is proposed for the detection of rotating mechanical nonlinear faults (such as rubbing, pedestal looseness. Under the phase space reconstructed by single vibration signal, the self-organization mapping (SOM with expectation maximization iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention. After that, the local tangent space alignment algorithm is adopted to compress the high-dimensional phase space into low-dimensional feature space. The proposed method takes advantages of the manifold learning in low-dimensional feature extraction and adaptive neighborhood construction of SOM and can extract intrinsic fault features of interest in two dimensional projection space. To evaluate the performance of the proposed method, the Lorenz system was simulated and rotation machinery with nonlinear faults was obtained for test purposes. Compared with the holospectrum approaches, the results reveal that the proposed method is superior in identifying faults and effective for rotating machinery condition monitoring.
Aspiras, Theus H.; Asari, Vijayan K.; Sakla, Wesam
2015-03-01
The human brain has the capability to process high quantities of data quickly for detection and recognition tasks. These tasks are made simpler by the understanding of data, which intentionally removes redundancies found in higher dimensional data and maps the data onto a lower dimensional space. The brain then encodes manifolds created in these spaces, which reveal a specific state of the system. We propose to use a recurrent neural network, the nonlinear line attractor (NLA) network, for the encoding of these manifolds as specific states, which will draw untrained data towards one of the specific states that the NLA network has encoded. We propose a Gaussian-weighted modular architecture for reducing the computational complexity of the conventional NLA network. The proposed architecture uses a neighborhood approach for establishing the interconnectivity of neurons to obtain the manifolds. The modified NLA network has been implemented and tested on the Electro-Optic Synthetic Vehicle Model Database created by the Air Force Research Laboratory (AFRL), which contains a vast array of high resolution imagery with several different lighting conditions and camera views. It is observed that the NLA network has the capability for representing high dimensional data for the recognition of the objects of interest through its new learning strategy. A nonlinear dimensionality reduction scheme based on singular value decomposition has found to be very effective in providing a low dimensional representation of the dataset. Application of the reduced dimensional space on the modified NLA algorithm would provide fast and more accurate recognition performance for real time applications.
Incremental Alignment Manifold Learning
Institute of Scientific and Technical Information of China (English)
Zhi Han; De-Yu Meng; Zong-Sen Xu; Nan-Nan Gu
2011-01-01
A new manifold learning method, called incremental alignment method (IAM), is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire dataset. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects: high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.
Zhang, Zhenyue; Wang, Jing; Zha, Hongyuan
2012-02-01
Manifold learning algorithms seek to find a low-dimensional parameterization of high-dimensional data. They heavily rely on the notion of what can be considered as local, how accurately the manifold can be approximated locally, and, last but not least, how the local structures can be patched together to produce the global parameterization. In this paper, we develop algorithms that address two key issues in manifold learning: 1) the adaptive selection of the local neighborhood sizes when imposing a connectivity structure on the given set of high-dimensional data points and 2) the adaptive bias reduction in the local low-dimensional embedding by accounting for the variations in the curvature of the manifold as well as its interplay with the sampling density of the data set. We demonstrate the effectiveness of our methods for improving the performance of manifold learning algorithms using both synthetic and real-world data sets.
Hierarchical manifold learning.
Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Jo; Rueckert, Daniel
2012-01-01
We present a novel method of hierarchical manifold learning which aims to automatically discover regional variations within images. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate its utility in two very different settings: (1) to learn the regional correlations in motion within a sequence of time-resolved images of the thoracic cavity; (2) to find discriminative regions of 3D brain images in the classification of neurodegenerative disease,
Manifold Regularized Reinforcement Learning.
Li, Hongliang; Liu, Derong; Wang, Ding
2017-01-27
This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.
Lin, Tong; Zha, Hongbin
2008-05-01
Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, i.e., how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low-dimensional space. Experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings.
Manifold Learning by Graduated Optimization.
Gashler, M; Ventura, D; Martinez, T
2011-12-01
We present an algorithm for manifold learning called manifold sculpting , which utilizes graduated optimization to seek an accurate manifold embedding. An empirical analysis across a wide range of manifold problems indicates that manifold sculpting yields more accurate results than a number of existing algorithms, including Isomap, locally linear embedding (LLE), Hessian LLE (HLLE), and landmark maximum variance unfolding (L-MVU), and is significantly more efficient than HLLE and L-MVU. Manifold sculpting also has the ability to benefit from prior knowledge about expected results.
Manifold learning based feature extraction for classification of hyper-spectral data
CSIR Research Space (South Africa)
Lunga, D
2013-08-01
Full Text Available often lie on sparse, nonlinear manifolds whose geometric and topological structures can be exploited via manifold learning techniques. In this article, we focused on demonstrating the opportunities provided by manifold learning for classification...
Learning Smooth Pattern Transformation Manifolds
Vural, Elif
2011-01-01
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. In order to construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold building problem, namely, approximation and classification. For the approximation problem, we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold. We present a DC (Difference-of-Convex) optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to transformation manifolds generated by rotation, translation and anisotropic scaling of a reference pattern. Then, we generalize this approach to a s...
Erem, B; Stovicek, P; Brooks, D H
2012-07-12
The dynamical structure of electrical recordings from the heart or torso surface is a valuable source of information about cardiac physiological behavior. In this paper, we use an existing data-driven technique for manifold identification to reveal electrophysiologically significant changes in the underlying dynamical structure of these signals. Our results suggest that this analysis tool characterizes and differentiates important parameters of cardiac bioelectric activity through their dynamic behavior, suggesting the potential to serve as an effective dynamic constraint in the context of inverse solutions.
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
Institute of Scientific and Technical Information of China (English)
张振跃; 查宏远
2004-01-01
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
Manifold learning based feature extraction for classification of hyperspectral data
CSIR Research Space (South Africa)
Lunga, D
2014-01-01
Full Text Available Interest in manifold learning for representing the topology of large, high dimensional nonlinear data sets in lower, but still meaningful dimensions for visualization and classification has grown rapidly over the past decade, and particularly...
基于流形学习的非线性维数约简方法%Nonlinear Dimensionality Reduction Method Based on Manifold Learning
Institute of Scientific and Technical Information of China (English)
段志臣; 芮小平; 张立媛
2012-01-01
流形学习是一种新的非线性维数约简方法,近年来正引起可视化等领域研究者的高度重视.为加深对流形学习的理解,介绍了流形学习的基本原理,总结了其研究进展和分类方法,最后阐述了几种常用的流形学习方法的基本思想、算法步骤和各自的优缺点.通过在人工数据集Swiss-Roll上进行实验,将各类方法在近邻值选取和噪声影响等方面进行了对比分析,结果表明:与传统的线性维数约简方法相比,流形学习方法能够有效地发现观测样本的低维结构.最后对流形学习未来的研究方向作出展望,以期在这一领域取得更大进展.%As a new kind of nonlinear dimensionality reduction method, manifold learning is capturing increasing interests of researchers. To understand manifold learning better, the principle is firstly introduced, and then its development history and different representations are summarized, finally several major method are introduced, whose basic thoughts, steps and advantages are pointed out respectively. By the experiments on Swiss-Roll, the selection of neighbors and noise effect are analyzed, the results shows: compared with traditional linear method, manifold learning can discover the intrinsic structure of the samples better. Finally the prospect of manifold learning was discussed for more developments.
Manifold Learning by Preserving Distance Orders.
Ataer-Cansizoglu, Esra; Akcakaya, Murat; Orhan, Umut; Erdogmus, Deniz
2014-03-01
Nonlinear dimensionality reduction is essential for the analysis and the interpretation of high dimensional data sets. In this manuscript, we propose a distance order preserving manifold learning algorithm that extends the basic mean-squared error cost function used mainly in multidimensional scaling (MDS)-based methods. We develop a constrained optimization problem by assuming explicit constraints on the order of distances in the low-dimensional space. In this optimization problem, as a generalization of MDS, instead of forcing a linear relationship between the distances in the high-dimensional original and low-dimensional projection space, we learn a non-decreasing relation approximated by radial basis functions. We compare the proposed method with existing manifold learning algorithms using synthetic datasets based on the commonly used residual variance and proposed percentage of violated distance orders metrics. We also perform experiments on a retinal image dataset used in Retinopathy of Prematurity (ROP) diagnosis.
Similarity Learning of Manifold Data.
Chen, Si-Bao; Ding, Chris H Q; Luo, Bin
2015-09-01
Without constructing adjacency graph for neighborhood, we propose a method to learn similarity among sample points of manifold in Laplacian embedding (LE) based on adding constraints of linear reconstruction and least absolute shrinkage and selection operator type minimization. Two algorithms and corresponding analyses are presented to learn similarity for mix-signed and nonnegative data respectively. The similarity learning method is further extended to kernel spaces. The experiments on both synthetic and real world benchmark data sets demonstrate that the proposed LE with new similarity has better visualization and achieves higher accuracy in classification.
Adaptive graph construction for Isomap manifold learning
Tran, Loc; Zheng, Zezhong; Zhou, Guoqing; Li, Jiang
2015-03-01
Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the l1 norm. The l1 enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than the classical approach. Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.
Manifold learning techniques and model reduction applied to dissipative PDEs
Sonday, Benjamin E; Gear, C William; Kevrekidis, Ioannis G
2010-01-01
We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a `"nonlinear extension" of the POD-Galerkin approach to obtaining reduced dynamic models of dissipative evolution equations. The approach is illustrated through a reaction-diffusion PDE, and the performance of different simulators on the full and the reduced models is compared. We also discuss the relation of this nonlinear extension with the so-called "nonlinear Galerkin" methods developed in the context of Approximate Inertial Manifolds.
Manifold learning in protein interactomes.
Marras, Elisabetta; Travaglione, Antonella; Capobianco, Enrico
2011-01-01
Many studies and applications in the post-genomic era have been devoted to analyze complex biological systems by computational inference methods. We propose to apply manifold learning methods to protein-protein interaction networks (PPIN). Despite their popularity in data-intensive applications, these methods have received limited attention in the context of biological networks. We show that there is both utility and unexplored potential in adopting manifold learning for network inference purposes. In particular, the following advantages are highlighted: (a) fusion with diagnostic statistical tools designed to assign significance to protein interactions based on pre-selected topological features; (b) dissection into components of the interactome in order to elucidate global and local connectivity organization; (c) relevance of embedding the interactome in reduced dimensions for biological validation purposes. We have compared the performances of three well-known techniques--kernel-PCA, RADICAL ICA, and ISOMAP--relatively to their power of mapping the interactome onto new coordinate dimensions where important associations among proteins can be detected, and then back projected such that the corresponding sub-interactomes are reconstructed. This recovery has been done selectively, by using significant information according to a robust statistical procedure, and then standard biological annotation has been provided to validate the results. We expect that a byproduct of using subspace analysis by the proposed techniques is a possible calibration of interactome modularity studies. Supplementary Material is available online at www.libertonlinec.com.
Characterizing pathological deviations from normality using constrained manifold-learning.
Duchateau, Nicolas; De Craene, Mathieu; Piella, Gemma; Frangi, Alejandro F
2011-01-01
We propose a technique to represent a pathological pattern as a deviation from normality along a manifold structure. Each subject is represented by a map of local motion abnormalities, obtained from a statistical atlas of motion built from a healthy population. The algorithm learns a manifold from a set of patients with varying degrees of the same pathology. The approach extends recent manifold-learning techniques by constraining the manifold to pass by a physiologically meaningful origin representing a normal motion pattern. Individuals are compared to the manifold population through a distance that combines a mapping to the manifold and the path along the manifold to reach its origin. The method is applied in the context of cardiac resynchronization therapy (CRT), focusing on a specific motion pattern of intra-ventricular dyssynchrony called septal flash (SF). We estimate the manifold from 50 CRT candidates with SF and test it on 38 CRT candidates and 21 healthy volunteers. Experiments highlight the need of nonlinear techniques to learn the studied data, and the relevance of the computed distance for comparing individuals to a specific pathological pattern.
Biomedical data analysis by supervised manifold learning.
Alvarez-Meza, A M; Daza-Santacoloma, G; Castellanos-Dominguez, G
2012-01-01
Biomedical data analysis is usually carried out by assuming that the information structure embedded into the biomedical recordings is linear, but that statement actually does not corresponds to the real behavior of the extracted features. In order to improve the accuracy of an automatic system to diagnostic support, and to reduce the computational complexity of the employed classifiers, we propose a nonlinear dimensionality reduction methodology based on manifold learning with multiple kernel representations, which learns the underlying data structure of biomedical information. Moreover, our approach can be used as a tool that allows the specialist to do a visual analysis and interpretation about the studied variables describing the health condition. Obtained results show how our approach maps the original high dimensional features into an embedding space where simple and straightforward classification strategies achieve a suitable system performance.
Manifold-based learning and synthesis.
Huang, Dong; Yi, Zhang; Pu, Xiaorong
2009-06-01
This paper proposes a new approach to analyze high-dimensional data set using low-dimensional manifold. This manifold-based approach provides a unified formulation for both learning from and synthesis back to the input space. The manifold learning method desires to solve two problems in many existing algorithms. The first problem is the local manifold distortion caused by the cost averaging of the global cost optimization during the manifold learning. The second problem results from the unit variance constraint generally used in those spectral embedding methods where global metric information is lost. For the out-of-sample data points, the proposed approach gives simple solutions to transverse between the input space and the feature space. In addition, this method can be used to estimate the underlying dimension and is robust to the number of neighbors. Experiments on both low-dimensional data and real image data are performed to illustrate the theory.
Non-linear Manifold Learning Algorithm Based on Intensity of Points%基于点密集度的非线性流形学习算法
Institute of Scientific and Technical Information of China (English)
黄淑萍
2012-01-01
This paper presents a non-linear manifold learning algorithm based on intensity of sample points. It proposes an effective intensity parameter of sample points, which constraints the low-dimensional embedding of uneven data well. There is a better embedding result than LLE. The experimental results on the artificial and face datasets show that the new algorithm yields a better embedding and classification result.%提出一种样本点密集度的非线性流形学习算法．该算法提出了一个有效的数据点密集参数，能够很好地对非均匀数据的低维嵌入进行约束，其嵌效结果明显优于LLE算法．在人工和人脸数据集上的实验结果表明，新算法产生了较好的嵌入及分类结果．
Hierarchical manifold learning for regional image analysis.
Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Joseph V; Rueckert, Daniel
2014-02-01
We present a novel method of hierarchical manifold learning which aims to automatically discover regional properties of image datasets. While traditional manifold learning methods have become widely used for dimensionality reduction in medical imaging, they suffer from only being able to consider whole images as single data points. We extend conventional techniques by additionally examining local variations, in order to produce spatially-varying manifold embeddings that characterize a given dataset. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate the utility of our method in two very different settings: 1) to learn the regional correlations in motion within a sequence of time-resolved MR images of the thoracic cavity; 2) to find discriminative regions of 3-D brain MR images associated with neurodegenerative disease.
Regional manifold learning for disease classification.
Ye, Dong Hye; Desjardins, Benoit; Hamm, Jihun; Litt, Harold; Pohl, Kilian M
2014-06-01
While manifold learning from images itself has become widely used in medical image analysis, the accuracy of existing implementations suffers from viewing each image as a single data point. To address this issue, we parcellate images into regions and then separately learn the manifold for each region. We use the regional manifolds as low-dimensional descriptors of high-dimensional morphological image features, which are then fed into a classifier to identify regions affected by disease. We produce a single ensemble decision for each scan by the weighted combination of these regional classification results. Each weight is determined by the regional accuracy of detecting the disease. When applied to cardiac magnetic resonance imaging of 50 normal controls and 50 patients with reconstructive surgery of Tetralogy of Fallot, our method achieves significantly better classification accuracy than approaches learning a single manifold across the entire image domain.
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Bhattacharjee, Satyaki; Matouš, Karel
2016-05-01
A new manifold-based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented. The model relies on a global geometric framework for nonlinear dimensionality reduction (Isomap), and the macroscopic loading parameters are linked to the reduced space using a Neural Network. The proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization. To construct the manifold, we perform a number of large three-dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver. The manifold-based reduced order model is verified using common principles from the machine-learning community. Both homogenization and localization of the multiscale solution are demonstrated on a large three-dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy.
Directory of Open Access Journals (Sweden)
M. Bauwens
2010-07-01
Full Text Available A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ^{18}O carbonate, which for freshwater influenced environments is hindered because the isotopic composition of the ambient water (related to salinity affects the reconstructed temperature. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: Firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information of other trace elements in multi-proxy models. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enabled a temperature reconstruction with a root mean squared error of ±2.19 °C for a salinity range between 15 and 32.
Manifold learning of brain MRIs by deep learning.
Brosch, Tom; Tam, Roger
2013-01-01
Manifold learning of medical images plays a potentially important role for modeling anatomical variability within a population with pplications that include segmentation, registration, and prediction of clinical parameters. This paper describes a novel method for learning the manifold of 3D brain images that, unlike most existing manifold learning methods, does not require the manifold space to be locally linear, and does not require a predefined similarity measure or a prebuilt proximity graph. Our manifold learning method is based on deep learning, a machine learning approach that uses layered networks (called deep belief networks, or DBNs) and has received much attention recently in the computer vision field due to their success in object recognition tasks. DBNs have traditionally been too computationally expensive for application to 3D images due to the large number of trainable parameters. Our primary contributions are (1) a much more computationally efficient training method for DBNs that makes training on 3D medical images with a resolution of up to 128 x 128 x 128 practical, and (2) the demonstration that DBNs can learn a low-dimensional manifold of brain volumes that detects modes of variations that correlate to demographic and disease parameters.
Directory of Open Access Journals (Sweden)
M. Bauwens
2010-11-01
Full Text Available A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ^{18}O carbonate. It is problematic in the case of freshwater influenced environments because the δ^{18}O isotopic composition of the ambient water (related to salinity needs to be known. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization (WDMR to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information for other trace elements in multi-proxy models. Although the models presented here are black-box models that do not use any prior knowledge about the proxies, the comparison of model reconstruction performances based on different proxy combinations do yield useful information about proxy characteristics. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enables a temperature reconstruction with a root mean squared error of ± 2.19 °C for a salinity range between 15 and 32.
Nonlinear control of chaotic systems:A switching manifold approach
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
2000-01-01
Full Text Available In this paper, a switching manifold approach is developed for nonlinear feed-back control of chaotic systems. The design strategy is straightforward, and the nonlinear control law is the simple bang–bang control. Yet, this control method is very effective; for instance, several desired equilibria can be stabilized by using one control law with different initial conditions. Its effectiveness is verified by both theoretical analysis and numerical simulations. The Lorenz system simulation is shown for the purpose of illustration.
Khan, Zulfiqar Hasan; Gu, Irene Yu-Hua
2013-12-01
This paper proposes a novel Bayesian online learning and tracking scheme for video objects on Grassmann manifolds. Although manifold visual object tracking is promising, large and fast nonplanar (or out-of-plane) pose changes and long-term partial occlusions of deformable objects in video remain a challenge that limits the tracking performance. The proposed method tackles these problems with the main novelties on: 1) online estimation of object appearances on Grassmann manifolds; 2) optimal criterion-based occlusion handling for online updating of object appearances; 3) a nonlinear dynamic model for both the appearance basis matrix and its velocity; and 4) Bayesian formulations, separately for the tracking process and the online learning process, that are realized by employing two particle filters: one is on the manifold for generating appearance particles and another on the linear space for generating affine box particles. Tracking and online updating are performed in an alternating fashion to mitigate the tracking drift. Experiments using the proposed tracker on videos captured by a single dynamic/static camera have shown robust tracking performance, particularly for scenarios when target objects contain significant nonplanar pose changes and long-term partial occlusions. Comparisons with eight existing state-of-the-art/most relevant manifold/nonmanifold trackers with evaluations have provided further support to the proposed scheme.
Manifold learning-based subspace distance for machinery damage assessment
Sun, Chuang; Zhang, Zhousuo; He, Zhengjia; Shen, Zhongjie; Chen, Binqiang
2016-03-01
Damage assessment is very meaningful to keep safety and reliability of machinery components, and vibration analysis is an effective way to carry out the damage assessment. In this paper, a damage index is designed by performing manifold distance analysis on vibration signal. To calculate the index, vibration signal is collected firstly, and feature extraction is carried out to obtain statistical features that can capture signal characteristics comprehensively. Then, manifold learning algorithm is utilized to decompose feature matrix to be a subspace, that is, manifold subspace. The manifold learning algorithm seeks to keep local relationship of the feature matrix, which is more meaningful for damage assessment. Finally, Grassmann distance between manifold subspaces is defined as a damage index. The Grassmann distance reflecting manifold structure is a suitable metric to measure distance between subspaces in the manifold. The defined damage index is applied to damage assessment of a rotor and the bearing, and the result validates its effectiveness for damage assessment of machinery component.
Regional manifold learning for deformable registration of brain MR images.
Ye, Dong Hye; Hamm, Jihun; Kwon, Dongjin; Davatzikos, Christos; Pohl, Kilian M
2012-01-01
We propose a method for deformable registration based on learning the manifolds of individual brain regions. Recent publications on registration of medical images advocate the use of manifold learning in order to confine the search space to anatomically plausible deformations. Existing methods construct manifolds based on a single metric over the entire image domain thus frequently miss regional brain variations. We address this issue by first learning manifolds for specific regions and then computing region-specific deformations from these manifolds. We then determine deformations for the entire image domain by learning the global manifold in such a way that it preserves the region-specific deformations. We evaluate the accuracy of our method by applying it to the LPBA40 dataset and measuring the overlap of the deformed segmentations. The result shows significant improvement in registration accuracy on cortex regions compared to other state of the art methods.
Out-of-Sample Generalizations for Supervised Manifold Learning for Classification
Vural, Elif; Guillemot, Christine
2016-03-01
Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes in the learned embedding. Most nonlinear supervised manifold learning methods compute the embedding of the manifolds only at the initially available training points, while the generalization of the embedding to novel points, known as the out-of-sample extension problem in manifold learning, becomes especially important in classification applications. In this work, we propose a semi-supervised method for building an interpolation function that provides an out-of-sample extension for general supervised manifold learning algorithms studied in the context of classification. The proposed algorithm computes a radial basis function (RBF) interpolator that minimizes an objective function consisting of the total embedding error of unlabeled test samples, defined as their distance to the embeddings of the manifolds of their own class, as well as a regularization term that controls the smoothness of the interpolation function in a direction-dependent way. The class labels of test data and the interpolation function parameters are estimated jointly with a progressive procedure. Experimental results on face and object images demonstrate the potential of the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets.
Manifold Regularized Experimental Design for Active Learning.
Zhang, Lining; Shum, Hubert P H; Shao, Ling
2016-12-02
Various machine learning and data mining tasks in classification require abundant data samples to be labeled for training. Conventional active learning methods aim at labeling the most informative samples for alleviating the labor of the user. Many previous studies in active learning select one sample after another in a greedy manner. However, this is not very effective because the classification models has to be retrained for each newly labeled sample. Moreover, many popular active learning approaches utilize the most uncertain samples by leveraging the classification hyperplane of the classifier, which is not appropriate since the classification hyperplane is inaccurate when the training data are small-sized. The problem of insufficient training data in real-world systems limits the potential applications of these approaches. This paper presents a novel method of active learning called manifold regularized experimental design (MRED), which can label multiple informative samples at one time for training. In addition, MRED gives an explicit geometric explanation for the selected samples to be labeled by the user. Different from existing active learning methods, our method avoids the intrinsic problems caused by insufficiently labeled samples in real-world applications. Various experiments on synthetic datasets, the Yale face database and the Corel image database have been carried out to show how MRED outperforms existing methods.
Learning an intrinsic-variable preserving manifold for dynamic visual tracking.
Qiao, Hong; Zhang, Peng; Zhang, Bo; Zheng, Suiwu
2010-06-01
Manifold learning is a hot topic in the field of computer science, particularly since nonlinear dimensionality reduction based on manifold learning was proposed in Science in 2000. The work has achieved great success. The main purpose of current manifold-learning approaches is to search for independent intrinsic variables underlying high dimensional inputs which lie on a low dimensional manifold. In this paper, a new manifold is built up in the training step of the process, on which the input training samples are set to be close to each other if the values of their intrinsic variables are close to each other. Then, the process of dimensionality reduction is transformed into a procedure of preserving the continuity of the intrinsic variables. By utilizing the new manifold, the dynamic tracking of a human who can move and rotate freely is achieved. From the theoretical point of view, it is the first approach to transfer the manifold-learning framework to dynamic tracking. From the application point of view, a new and low dimensional feature for visual tracking is obtained and successfully applied to the real-time tracking of a free-moving object from a dynamic vision system. Experimental results from a dynamic tracking system which is mounted on a dynamic robot validate the effectiveness of the new algorithm.
A manifold learning approach to target detection in high-resolution hyperspectral imagery
Ziemann, Amanda K.
Imagery collected from airborne platforms and satellites provide an important medium for remotely analyzing the content in a scene. In particular, the ability to detect a specific material within a scene is of high importance to both civilian and defense applications. This may include identifying "targets" such as vehicles, buildings, or boats. Sensors that process hyperspectral images provide the high-dimensional spectral information necessary to perform such analyses. However, for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data; this is particularly true when implementing traditional target detection approaches, and the limitations of these models are well-documented. With manifold learning based approaches, the only assumption is that the data reside on an underlying manifold that can be discretely modeled by a graph. The research presented here focuses on the use of graph theory and manifold learning in hyperspectral imagery. Early work explored various graph-building techniques with application to the background model of the Topological Anomaly Detection (TAD) algorithm, which is a graph theory based approach to anomaly detection. This led towards a focus on target detection, and in the development of a specific graph-based model of the data and subsequent dimensionality reduction using manifold learning. An adaptive graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation; the artificial target manifold helps to guide the
Model Transport: Towards Scalable Transfer Learning on Manifolds
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Black, Michael J.
2014-01-01
“commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image......We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...
The approximate weak inertial manifolds of a class of nonlinear hyperbolic dynamical systems
Institute of Scientific and Technical Information of China (English)
赵怡
1996-01-01
Some concepts about approximate and semi-approximate weak inertial manifolds are introduced and the existence of global attractor and semi-approximate weak inertial manifolds is obtained for a class of nonlinear hyperbolic dynamical systems by means of some topologically homeomorphic mappings and techniques. Using these results, the existence of approximate weak inertial manifolds is also presented for a kind of nonlinear hyperbolic system arising from relativistic quantum mechanics. The regularization problem is proposed finally.
Constrained manifold learning for the characterization of pathological deviations from normality.
Duchateau, Nicolas; De Craene, Mathieu; Piella, Gemma; Frangi, Alejandro F
2012-12-01
This paper describes a technique to (1) learn the representation of a pathological motion pattern from a given population, and (2) compare individuals to this population. Our hypothesis is that this pattern can be modeled as a deviation from normal motion by means of non-linear embedding techniques. Each subject is represented by a 2D map of local motion abnormalities, obtained from a statistical atlas of myocardial motion built from a healthy population. The algorithm estimates a manifold from a set of patients with varying degrees of the same disease, and compares individuals to the training population using a mapping to the manifold and a distance to normality along the manifold. The approach extends recent manifold learning techniques by constraining the manifold to pass by a physiologically meaningful origin representing a normal motion pattern. Interpolation techniques using locally adjustable kernel improve the accuracy of the method. The technique is applied in the context of cardiac resynchronization therapy (CRT), focusing on a specific motion pattern of intra-ventricular dyssynchrony called septal flash (SF). We estimate the manifold from 50 CRT candidates with SF and test it on 37 CRT candidates and 21 healthy volunteers. Experiments highlight the relevance of non-linear techniques to model a pathological pattern from the training set and compare new individuals to this pattern.
A new embedding quality assessment method for manifold learning
Zhang, Peng; Zhang, Bo
2011-01-01
Manifold learning is a hot research topic in the field of computer science. A crucial issue with current manifold learning methods is that they lack a natural quantitative measure to assess the quality of learned embeddings, which greatly limits their applications to real-world problems. In this paper, a new embedding quality assessment method for manifold learning, named as Normalization Independent Embedding Quality Assessment (NIEQA), is proposed. Compared with current assessment methods which are limited to isometric embeddings, the NIEQA method has a much larger application range due to two features. First, it is based on a new measure which can effectively evaluate how well local neighborhood geometry is preserved under normalization, hence it can be applied to both isometric and normalized embeddings. Second, it can provide both local and global evaluations to output an overall assessment. Therefore, NIEQA can serve as a natural tool in model selection and evaluation tasks for manifold learning. Experi...
Manifold learning based registration algorithms applied to multimodal images.
Azampour, Mohammad Farid; Ghaffari, Aboozar; Hamidinekoo, Azam; Fatemizadeh, Emad
2014-01-01
Manifold learning algorithms are proposed to be used in image processing based on their ability in preserving data structures while reducing the dimension and the exposure of data structure in lower dimension. Multi-modal images have the same structure and can be registered together as monomodal images if only structural information is shown. As a result, manifold learning is able to transform multi-modal images to mono-modal ones and subsequently do the registration using mono-modal methods. Based on this application, in this paper novel similarity measures are proposed for multi-modal images in which Laplacian eigenmaps are employed as manifold learning algorithm and are tested against rigid registration of PET/MR images. Results show the feasibility of using manifold learning as a way of calculating the similarity between multimodal images.
Spatial context driven manifold learning for hyperspectral image classification
CSIR Research Space (South Africa)
Zhang, Y
2014-06-01
Full Text Available Manifold learning techniques have demonstrated various levels of success in their ability to represent spectral signature characteristics in hyperspectral imagery. Such images consists of spectral features with very subtle differences and at times...
A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article the concept of local conjugation of a C1 mapping between two Banach manifolds is introduced. Then a rank theorem for nonlinear semi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis.
A comparative study on manifold learning of hyperspectral data for land cover classification
Ozturk, Ceyda Nur; Bilgin, Gokhan
2015-03-01
This paper focuses on the land cover classification problem by employing a number of manifold learning algorithms in the feature extraction phase, then by running single and ensemble of classifiers in the modeling phase. Manifolds are learned on training samples selected randomly within available data, while the transformation of the remaining test samples is realized for linear and nonlinear methods via the learnt mappings and a radial-basis function neural network based interpolation method, respectively. The classification accuracies of the original data and the embedded manifolds are investigated with several classifiers. Experimental results on a 200-band hyperspectral image indicated that support vector machine was the best classifier for most of the methods, being nearly as accurate as the best classification rate of the original data. Furthermore, our modified version of random subspace classifier could even outperform the classification accuracy of the original data for local Fisher's discriminant analysis method despite of a considerable decrease in the extrinsic dimension.
Interpolation-based reduced-order modelling for steady transonic flows via manifold learning
DEFF Research Database (Denmark)
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2014-01-01
This paper presents a parametric reduced-order model (ROM) based on manifold learning (ML) for use in steady transonic aerodynamic applications. The main objective of this work is to derive an efficient ROM that exploits the low-dimensional nonlinear solution manifold to ensure an improved...... that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method to capture the variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced...
Hierarchical discriminant manifold learning for dimensionality reduction and image classification
Chen, Weihai; Zhao, Changchen; Ding, Kai; Wu, Xingming; Chen, Peter C. Y.
2015-09-01
In the field of image classification, it has been a trend that in order to deliver a reliable classification performance, the feature extraction model becomes increasingly more complicated, leading to a high dimensionality of image representations. This, in turn, demands greater computation resources for image classification. Thus, it is desirable to apply dimensionality reduction (DR) methods for image classification. It is necessary to apply DR methods to relieve the computational burden as well as to improve the classification accuracy. However, traditional DR methods are not compatible with modern feature extraction methods. A framework that combines manifold learning based DR and feature extraction in a deeper way for image classification is proposed. A multiscale cell representation is extracted from the spatial pyramid to satisfy the locality constraints for a manifold learning method. A spectral weighted mean filtering is proposed to eliminate noise in the feature space. A hierarchical discriminant manifold learning is proposed which incorporates both category label and image scale information to guide the DR process. Finally, the image representation is generated by concatenating dimensionality reduced cell representations from the same image. Extensive experiments are conducted to test the proposed algorithm on both scene and object recognition datasets in comparison with several well-established and state-of-the-art methods with respect to classification precision and computational time. The results verify the effectiveness of incorporating manifold learning in the feature extraction procedure and imply that the multiscale cell representations may be distributed on a manifold.
[A new algorithm for NIR modeling based on manifold learning].
Hong, Ming-Jian; Wen, Zhi-Yu; Zhang, Xiao-Hong; Wen, Quan
2009-07-01
Manifold learning is a new kind of algorithm originating from the field of machine learning to find the intrinsic dimensionality of numerous and complex data and to extract most important information from the raw data to develop a regression or classification model. The basic assumption of the manifold learning is that the high-dimensional data measured from the same object using some devices must reside on a manifold with much lower dimensions determined by a few properties of the object. While NIR spectra are characterized by their high dimensions and complicated band assignment, the authors may assume that the NIR spectra of the same kind of substances with different chemical concentrations should reside on a manifold with much lower dimensions determined by the concentrations, according to the above assumption. As one of the best known algorithms of manifold learning, locally linear embedding (LLE) further assumes that the underlying manifold is locally linear. So, every data point in the manifold should be a linear combination of its neighbors. Based on the above assumptions, the present paper proposes a new algorithm named least square locally weighted regression (LS-LWR), which is a kind of LWR with weights determined by the least squares instead of a predefined function. Then, the NIR spectra of glucose solutions with various concentrations are measured using a NIR spectrometer and LS-LWR is verified by predicting the concentrations of glucose solutions quantitatively. Compared with the existing algorithms such as principal component regression (PCR) and partial least squares regression (PLSR), the LS-LWR has better predictability measured by the standard error of prediction (SEP) and generates an elegant model with good stability and efficiency.
Why Deep Learning Works: A Manifold Disentanglement Perspective.
Brahma, Pratik Prabhanjan; Wu, Dapeng; She, Yiyuan
2016-10-01
Deep hierarchical representations of the data have been found out to provide better informative features for several machine learning applications. In addition, multilayer neural networks surprisingly tend to achieve better performance when they are subject to an unsupervised pretraining. The booming of deep learning motivates researchers to identify the factors that contribute to its success. One possible reason identified is the flattening of manifold-shaped data in higher layers of neural networks. However, it is not clear how to measure the flattening of such manifold-shaped data and what amount of flattening a deep neural network can achieve. For the first time, this paper provides quantitative evidence to validate the flattening hypothesis. To achieve this, we propose a few quantities for measuring manifold entanglement under certain assumptions and conduct experiments with both synthetic and real-world data. Our experimental results validate the proposition and lead to new insights on deep learning.
Latent common manifold learning with alternating diffusion: analysis and applications
Talmon, Ronen
2016-01-01
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We introduce a latent common manifold model underlying multiple sensor observations for the purpose of multimodal data fusion. A method based on alternating diffusion is presented and analyzed; we provide theoretical analysis of the method under the latent common manifold model. To exemplify the power of the proposed framework, experimental results in several applications are reported.
A New Method for Intrusion Detection using Manifold Learning Algorithm
Directory of Open Access Journals (Sweden)
Guoping Hou
2013-07-01
Full Text Available Computer and network security has received and will still receive much attention. Any unexpected intrusion will damage the network. It is therefore imperative to detect the network intrusion to ensure the normal operation of the internet. There are many studies in the intrusion detection and intrusion patter recognition. The artificial neural network (ANN has proven to be powerful for the intrusion detection. However, very little work has discussed the optimization of the input intrusion features for the ANN. Generally, the intrusion features contain a certain number of useless features, which is useless for the intrusion detection. Large dimensions of the feature data will also affect the intrusion detection performance of the ANN. In order to improve the ANN performance, a new approach for network intrusion detection based on nonlinear feature dimension reduction and ANN is proposed in this work. The manifold learning algorithm was used to reduce the intrusion feature vector. Then an ANN classifier was employed to identify the intrusion. The efficiency of the proposed method was evaluated with the real intrusion data. The test result shows that the proposed approach has good intrusion detection performance.
Manifold Learning for Biomarker Discovery in MR Imaging
Wolz, Robin; Aljabar, Paul; Hajnal, Joseph V.; Rueckert, Daniel
We propose a framework for the extraction of biomarkers from low-dimensional manifolds representing inter- and intra-subject brain variation in MR image data. The coordinates of each image in such a low-dimensional space captures information about structural shape and appearance and, when a phenotype exists, about the subject's clinical state. A key contribution is that we propose a method for incorporating longitudinal image information in the learned manifold. In particular, we compare simultaneously embedding baseline and follow-up scans into a single manifold with the combination of separate manifold representations for inter-subject and intra-subject variation. We apply the proposed methods to 362 subjects enrolled in the Alzheimer's Disease Neuroimaging Initiative (ADNI) and classify healthy controls, subjects with Alzheimer's disease (AD) and subjects with mild cognitive impairment (MCI). Learning manifolds based on both the appearance and temporal change of the hippocampus, leads to correct classification rates comparable with those provided by state-of-the-art automatic segmentation estimates of hippocampal volume and atrophy. The biomarkers identified with the proposed method are data-driven and represent a potential alternative to a-priori defined biomarkers derived from manual or automated segmentations.
Manifold learning approach for chaos in the dripping faucet.
Suetani, Hiromichi; Soejima, Karin; Matsuoka, Rei; Parlitz, Ulrich; Hata, Hiroki
2012-09-01
Dripping water from a faucet is a typical example exhibiting rich nonlinear phenomena. For such a system, the time stamps at which water drops separate from the faucet can be directly observed in real experiments, and the time series of intervals τn between drop separations becomes a subject of analysis. Even if the mass mn of a drop at the onset of the nth separation, which is difficult to observe experimentally, exhibits perfectly deterministic dynamics, it may be difficult to obtain the same information about the underlying dynamics from the time series τn. This is because the return plot τn-1 vs. τn may become a multivalued relation (i.e., it doesn't represent a function describing deterministic dynamics). In this paper, we propose a method to construct a nonlinear coordinate which provides a "surrogate" of the internal state mn from the time series of τn. Here, a key of the proposed approach is to use isomap, which is a well-known method of manifold learning. We first apply it to the time series of τn generated from the numerical simulation of a phenomenological mass-spring model for the dripping faucet system. It is shown that a clear one-dimensional map is obtained by the proposed approach, whose characteristic quantities such as the Lyapunov exponent, the topological entropy, and the time correlation function coincide with the original dripping faucet system. Furthermore, we also analyze data obtained from real dripping faucet experiments, which also provide promising results.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
Suzuki, Hidetoshi; Sakamoto, Noboru; Celikovský, Sergej
In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.
Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems
Qudrat Khan; Aamer Iqbal Bhatti; Antonella Ferrara
2014-01-01
An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In c...
Gifani, Parisa; Behnam, Hamid; Shalbaf, Ahmad; Sani, Zahra Alizadeh
2010-09-01
The automatic detection of end-diastole and end-systole frames of echocardiography images is the first step for calculation of the ejection fraction, stroke volume and some other features related to heart motion abnormalities. In this paper, the manifold learning algorithm is applied on 2D echocardiography images to find out the relationship between the frames of one cycle of heart motion. By this approach the nonlinear embedded information in sequential images is represented in a two-dimensional manifold by the LLE algorithm and each image is depicted by a point on reconstructed manifold. There are three dense regions on the manifold which correspond to the three phases of cardiac cycle ('isovolumetric contraction', 'isovolumetric relaxation', 'reduced filling'), wherein there is no prominent change in ventricular volume. By the fact that the end-systolic and end-diastolic frames are in isovolumic phases of the cardiac cycle, the dense regions can be used to find these frames. By calculating the distance between consecutive points in the manifold, the isovolumic frames are mapped on the three minimums of the distance diagrams which were used to select the corresponding images. The minimum correlation between these images leads to detection of end-systole and end-diastole frames. The results on six healthy volunteers have been validated by an experienced echo cardiologist and depict the usefulness of the presented method.
Learning the manifold of quality ultrasound acquisition.
El-Zehiry, Noha; Yan, Michelle; Good, Sara; Fang, Tong; Zhou, S Kevin; Grady, Leo
2013-01-01
Ultrasound acquisition is a challenging task that requires simultaneous adjustment of several acquisition parameters (the depth, the focus, the frequency and its operation mode). If the acquisition parameters are not properly chosen, the resulting image will have a poor quality and will degrade the patient diagnosis and treatment workflow. Several hardware-based systems for autotuning the acquisition parameters have been previously proposed, but these solutions were largely abandoned because they failed to properly account for tissue inhomogeneity and other patient-specific characteristics. Consequently, in routine practice the clinician either uses population-based parameter presets or manually adjusts the acquisition parameters for each patient during the scan. In this paper, we revisit the problem of autotuning the acquisition parameters by taking a completely novel approach and producing a solution based on image analytics. Our solution is inspired by the autofocus capability of conventional digital cameras, but is significantly more challenging because the number of acquisition parameters is large and the determination of "good quality" images is more difficult to assess. Surprisingly, we show that the set of acquisition parameters which produce images that are favored by clinicians comprise a 1D manifold, allowing for a real-time optimization to maximize image quality. We demonstrate our method for acquisition parameter autotuning on several live patients, showing that our system can start with a poor initial set of parameters and automatically optimize the parameters to produce high quality images.
Sampling from Determinantal Point Processes for Scalable Manifold Learning.
Wachinger, Christian; Golland, Polina
2015-01-01
High computational costs of manifold learning prohibit its application for large datasets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the Nyström method. The two main challenges that arise are: (i) the landmarks selected in non-Euclidean geometries must result in a low reconstruction error, (ii) the graph constructed from sparsely sampled landmarks must approximate the manifold well. We propose to sample the landmarks from determinantal distributions on non-Euclidean spaces. Since current determinantal sampling algorithms have the same complexity as those for manifold learning, we present an efficient approximation with linear complexity. Further, we recover the local geometry after the sparsification by assigning each landmark a local covariance matrix, estimated from the original point set. The resulting neighborhood selection .based on the Bhattacharyya distance improves the embedding of sparsely sampled manifolds. Our experiments show a significant performance improvement compared to state-of-the-art landmark selection techniques on synthetic and medical data.
Hira, Zena M; Trigeorgis, George; Gillies, Duncan F
2014-01-01
Microarray databases are a large source of genetic data, which, upon proper analysis, could enhance our understanding of biology and medicine. Many microarray experiments have been designed to investigate the genetic mechanisms of cancer, and analytical approaches have been applied in order to classify different types of cancer or distinguish between cancerous and non-cancerous tissue. However, microarrays are high-dimensional datasets with high levels of noise and this causes problems when using machine learning methods. A popular approach to this problem is to search for a set of features that will simplify the structure and to some degree remove the noise from the data. The most widely used approach to feature extraction is principal component analysis (PCA) which assumes a multivariate Gaussian model of the data. More recently, non-linear methods have been investigated. Among these, manifold learning algorithms, for example Isomap, aim to project the data from a higher dimensional space onto a lower dimension one. We have proposed a priori manifold learning for finding a manifold in which a representative set of microarray data is fused with relevant data taken from the KEGG pathway database. Once the manifold has been constructed the raw microarray data is projected onto it and clustering and classification can take place. In contrast to earlier fusion based methods, the prior knowledge from the KEGG databases is not used in, and does not bias the classification process--it merely acts as an aid to find the best space in which to search the data. In our experiments we have found that using our new manifold method gives better classification results than using either PCA or conventional Isomap.
Robust head pose estimation via supervised manifold learning.
Wang, Chao; Song, Xubo
2014-05-01
Head poses can be automatically estimated using manifold learning algorithms, with the assumption that with the pose being the only variable, the face images should lie in a smooth and low-dimensional manifold. However, this estimation approach is challenging due to other appearance variations related to identity, head location in image, background clutter, facial expression, and illumination. To address the problem, we propose to incorporate supervised information (pose angles of training samples) into the process of manifold learning. The process has three stages: neighborhood construction, graph weight computation and projection learning. For the first two stages, we redefine inter-point distance for neighborhood construction as well as graph weight by constraining them with the pose angle information. For Stage 3, we present a supervised neighborhood-based linear feature transformation algorithm to keep the data points with similar pose angles close together but the data points with dissimilar pose angles far apart. The experimental results show that our method has higher estimation accuracy than the other state-of-art algorithms and is robust to identity and illumination variations.
Local matrix learning in clustering and applications for manifold visualization.
Arnonkijpanich, Banchar; Hasenfuss, Alexander; Hammer, Barbara
2010-05-01
Electronic data sets are increasing rapidly with respect to both, size of the data sets and data resolution, i.e. dimensionality, such that adequate data inspection and data visualization have become central issues of data mining. In this article, we present an extension of classical clustering schemes by local matrix adaptation, which allows a better representation of data by means of clusters with an arbitrary spherical shape. Unlike previous proposals, the method is derived from a global cost function. The focus of this article is to demonstrate the applicability of this matrix clustering scheme to low-dimensional data embedding for data inspection. The proposed method is based on matrix learning for neural gas and manifold charting. This provides an explicit mapping of a given high-dimensional data space to low dimensionality. We demonstrate the usefulness of this method for data inspection and manifold visualization.
Institute of Scientific and Technical Information of China (English)
王泽杰
2008-01-01
流形学习(Manifold Learning)算法是近年来发展起来的非线性降维机器学习算法.目前的流形学习算法大体可以分为两类:全局的(如等度规映射)和局部的(如局部线性嵌套),它们有各自的优点和不足.以等度规映射(ISOMAP)和局部线性嵌套(LLE)为例,通过实验比较分析了这两类算法在参数选择、前提条件和执行效率上的特点,期望为不同应用提供参考.
Unsupervised single-particle deep classification via statistical manifold learning
Wu, Jiayi; Condgon, Charles; Brett, Bevin; Chen, Shuobing; Ouyang, Qi; Mao, Youdong
2016-01-01
Structural heterogeneity in single-particle images presents a major challenge for high-resolution cryo-electron microscopy (cryo-EM) structure determination. Here we introduce a statistical manifold learning approach for unsupervised single-particle deep classification. When optimized for Intel high-performance computing (HPC) processors, our approach can generate thousands of reference-free class averages within several hours from hundreds of thousands of single-particle cryo-EM images. Deep classification thus assists in computational purification of single-particle datasets for high-resolution reconstruction.
Semi-Supervised Learning Based on Manifold in BCI
Institute of Scientific and Technical Information of China (English)
Ji-Ying Zhong; Xu Lei; De-Zhong Yao
2009-01-01
A Laplacian support vector machine (LapSVM) algorithm,a semi-supervised learning based on manifold,is introduced to brain-computer interface (BCI) to raise the classification precision and reduce the subjects' training complexity.The data are collected from three subjects in a three-task mental imagery experiment.LapSVM and transductive SVM (TSVM) are trained with a few labeled samples and a large number of unlabeled samples.The results confirm that LapSVM has a much better classification than TSVM.
Dictionary Pair Learning on Grassmann Manifolds for Image Denoising.
Zeng, Xianhua; Bian, Wei; Liu, Wei; Shen, Jialie; Tao, Dacheng
2015-11-01
Image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real-world applications. The traditional patch-based and sparse coding-driven image denoising methods convert 2D image patches into 1D vectors for further processing. Thus, these methods inevitably break down the inherent 2D geometric structure of natural images. To overcome this limitation pertaining to the previous image denoising methods, we propose a 2D image denoising model, namely, the dictionary pair learning (DPL) model, and we design a corresponding algorithm called the DPL on the Grassmann-manifold (DPLG) algorithm. The DPLG algorithm first learns an initial dictionary pair (i.e., the left and right dictionaries) by employing a subspace partition technique on the Grassmann manifold, wherein the refined dictionary pair is obtained through a sub-dictionary pair merging. The DPLG obtains a sparse representation by encoding each image patch only with the selected sub-dictionary pair. The non-zero elements of the sparse representation are further smoothed by the graph Laplacian operator to remove the noise. Consequently, the DPLG algorithm not only preserves the inherent 2D geometric structure of natural images but also performs manifold smoothing in the 2D sparse coding space. We demonstrate that the DPLG algorithm also improves the structural SIMilarity values of the perceptual visual quality for denoised images using the experimental evaluations on the benchmark images and Berkeley segmentation data sets. Moreover, the DPLG also produces the competitive peak signal-to-noise ratio values from popular image denoising algorithms.
Manifold-Based Reinforcement Learning via Locally Linear Reconstruction.
Xu, Xin; Huang, Zhenhua; Zuo, Lei; He, Haibo
2017-04-01
Feature representation is critical not only for pattern recognition tasks but also for reinforcement learning (RL) methods to solve learning control problems under uncertainties. In this paper, a manifold-based RL approach using the principle of locally linear reconstruction (LLR) is proposed for Markov decision processes with large or continuous state spaces. In the proposed approach, an LLR-based feature learning scheme is developed for value function approximation in RL, where a set of smooth feature vectors is generated by preserving the local approximation properties of neighboring points in the original state space. By using the proposed feature learning scheme, an LLR-based approximate policy iteration (API) algorithm is designed for learning control problems with large or continuous state spaces. The relationship between the value approximation error of a new data point and the estimated values of its nearest neighbors is analyzed. In order to compare different feature representation and learning approaches for RL, a comprehensive simulation and experimental study was conducted on three benchmark learning control problems. It is illustrated that under a wide range of parameter settings, the LLR-based API algorithm can obtain better learning control performance than the previous API methods with different feature representation schemes.
Institute of Scientific and Technical Information of China (English)
LIU Xiaofeng; ZHAO Lei
2012-01-01
Stable operation of aircraft engine compressions is constrained by rotating surge.In this paper,an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is presented.Firstly,this paper gives an overview of the current state of modeling aerodynamic flow instabilities in engine compressors.Secondly,the expansion form of equilibrium manifold is introduced,and the choosing scheduling variable method is discussed.Then,this paper also gives the identification procedure of modeling the approximate nonlinear model.Finally,the modeling and simulations with high pressure (HP) compressor surge margin of the aircraft engine show that this real-time model has the same accuracy with the thermodynamic model,but has simpler structure and shorter computation time.
Applying manifold learning to plotting approximate contour trees.
Takahashi, Shigeo; Fujishiro, Issei; Okada, Masato
2009-01-01
A contour tree is a powerful tool for delineating the topological evolution of isosurfaces of a single-valued function, and thus has been frequently used as a means of extracting features from volumes and their time-varying behaviors. Several sophisticated algorithms have been proposed for constructing contour trees while they often complicate the software implementation especially for higher-dimensional cases such as time-varying volumes. This paper presents a simple yet effective approach to plotting in 3D space, approximate contour trees from a set of scattered samples embedded in the high-dimensional space. Our main idea is to take advantage of manifold learning so that we can elongate the distribution of high-dimensional data samples to embed it into a low-dimensional space while respecting its local proximity of sample points. The contribution of this paper lies in the introduction of new distance metrics to manifold learning, which allows us to reformulate existing algorithms as a variant of currently available dimensionality reduction scheme. Efficient reduction of data sizes together with segmentation capability is also developed to equip our approach with a coarse-to-fine analysis even for large-scale datasets. Examples are provided to demonstrate that our proposed scheme can successfully traverse the features of volumes and their temporal behaviors through the constructed contour trees.
Manifold regularized multitask feature learning for multimodality disease classification.
Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang
2015-02-01
Multimodality based methods have shown great advantages in classification of Alzheimer's disease (AD) and its prodromal stage, that is, mild cognitive impairment (MCI). Recently, multitask feature selection methods are typically used for joint selection of common features across multiple modalities. However, one disadvantage of existing multimodality based methods is that they ignore the useful data distribution information in each modality, which is essential for subsequent classification. Accordingly, in this paper we propose a manifold regularized multitask feature learning method to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality. Specifically, we denote the feature learning on each modality as a single task, and use group-sparsity regularizer to capture the intrinsic relatedness among multiple tasks (i.e., modalities) and jointly select the common features from multiple tasks. Furthermore, we introduce a new manifold-based Laplacian regularizer to preserve the data distribution information from each task. Finally, we use the multikernel support vector machine method to fuse multimodality data for eventual classification. Conversely, we also extend our method to the semisupervised setting, where only partial data are labeled. We evaluate our method using the baseline magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET), and cerebrospinal fluid (CSF) data of subjects from AD neuroimaging initiative database. The experimental results demonstrate that our proposed method can not only achieve improved classification performance, but also help to discover the disease-related brain regions useful for disease diagnosis.
A New Method for Pseudo-increasing Frame Rates of Echocardiography Images Using Manifold Learning.
Gifani, Parisa; Behnam, Hamid; Sani, Zahra Alizadeh
2011-05-01
Increasing frame rate is a challenging issue for better interpretation of medical images and diagnosis based on tracking the small transient motions of myocardium and valves in real time visualization. In this paper, manifold learning algorithm is applied to extract the nonlinear embedded information about echocardiography images from the consecutive images in two dimensional manifold spaces. In this method, we presume that the dimensionality of echocardiography images obtained from a patient is artificially high and the images can be described as functions of only a few underlying parameters such as periodic motion due to heartbeat. By this approach, each image is projected as a point on the reconstructed manifold; hence, the relationship between images in the new domain can be obtained according to periodicity of the heart cycle. To have a better tracking of the echocardiography, images during the fast motions of heart we have rearranged the similar frames of consecutive heart cycles in a sequence. This provides a full view slow motion of heart movement through increasing the frame rate to three times the traditional ultrasound systems.
Scene recognition by manifold regularized deep learning architecture.
Yuan, Yuan; Mou, Lichao; Lu, Xiaoqiang
2015-10-01
Scene recognition is an important problem in the field of computer vision, because it helps to narrow the gap between the computer and the human beings on scene understanding. Semantic modeling is a popular technique used to fill the semantic gap in scene recognition. However, most of the semantic modeling approaches learn shallow, one-layer representations for scene recognition, while ignoring the structural information related between images, often resulting in poor performance. Modeled after our own human visual system, as it is intended to inherit humanlike judgment, a manifold regularized deep architecture is proposed for scene recognition. The proposed deep architecture exploits the structural information of the data, making for a mapping between visible layer and hidden layer. By the proposed approach, a deep architecture could be designed to learn the high-level features for scene recognition in an unsupervised fashion. Experiments on standard data sets show that our method outperforms the state-of-the-art used for scene recognition.
Tang, Xiao-yan; Gao, Kun; Ni, Guo-qiang; Zhu, Zhen-yu; Cheng, Hao-bo
2013-09-01
An improved N-FINDR endmember extraction algorithm by combining manifold learning and spatial information is presented under nonlinear mixing assumptions. Firstly, adaptive local tangent space alignment is adapted to seek potential intrinsic low-dimensional structures of hyperspectral high-diemensional data and reduce original data into a low-dimensional space. Secondly, spatial preprocessing is used by enhancing each pixel vector in spatially homogeneous areas, according to the continuity of spatial distribution of the materials. Finally, endmembers are extracted by looking for the largest simplex volume. The proposed method can increase the precision of endmember extraction by solving the nonlinearity of hyperspectral data and taking advantage of spatial information. Experimental results on simulated and real hyperspectral data demonstrate that the proposed approach outperformed the geodesic simplex volume maximization (GSVM), vertex component analysis (VCA) and spatial preprocessing N-FINDR method (SPPNFINDR).
Feature selection and multi-kernel learning for sparse representation on a manifold.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2014-03-01
Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao et al. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods.
Feature selection and multi-kernel learning for sparse representation on a manifold
Wang, Jim Jing-Yan
2014-03-01
Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao etal. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. © 2013 Elsevier Ltd.
Ho, Shen-Shyang; Dai, Peng; Rudzicz, Frank
2016-06-01
Multivariate variable-length sequence data are becoming ubiquitous with the technological advancement in mobile devices and sensor networks. Such data are difficult to compare, visualize, and analyze due to the nonmetric nature of data sequence similarity measures. In this paper, we propose a general manifold learning framework for arbitrary-length multivariate data sequences driven by similarity/distance (parameter) learning in both the original data sequence space and the learned manifold. Our proposed algorithm transforms the data sequences in a nonmetric data sequence space into feature vectors in a manifold that preserves the data sequence space structure. In particular, the feature vectors in the manifold representing similar data sequences remain close to one another and far from the feature points corresponding to dissimilar data sequences. To achieve this objective, we assume a semisupervised setting where we have knowledge about whether some of data sequences are similar or dissimilar, called the instance-level constraints. Using this information, one learns the similarity measure for the data sequence space and the distance measures for the manifold. Moreover, we describe an approach to handle the similarity search problem given user-defined instance level constraints in the learned manifold using a consensus voting scheme. Experimental results on both synthetic data and real tropical cyclone sequence data are presented to demonstrate the feasibility of our manifold learning framework and the robustness of performing similarity search in the learned manifold.
Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction
Institute of Scientific and Technical Information of China (English)
Li Yu-Mei; Guan Xin-Ping
2009-01-01
Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique,nonlinear consensus protocols are presented.We prove that a group of agents can reach a β-consensus,the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents.Moreover,we derive the conditions to guarantee that all the agents reach a β-consensus on a desired group decision value.Finally,a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed.Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.
Rangraz, Parisa; Behnam, Hamid; Sobhebidari, Pooya; Tavakkoli, Jahan
2014-12-01
High-intensity focused ultrasound (HIFU) induces thermal lesions by increasing the tissue temperature in a tight focal region. The main ultrasound imaging techniques currently used to monitor HIFU treatment are standard pulse-echo B-mode ultrasound imaging, ultrasound temperature estimation and elastography-based methods. The present study was carried out on ex vivo animal tissue samples, in which backscattered radiofrequency (RF) signals were acquired in real time at time instances before, during and after HIFU treatment. The manifold learning algorithm, a non-linear dimensionality reduction method, was applied to RF signals whichconstruct B-mode images to detect the HIFU-induced changes among the image frames obtained during HIFU treatment. In this approach, the embedded non-linear information in the region of interest of sequential images is represented in a 2-D manifold with the Isomap algorithm, and each image is depicted as a point on the reconstructed manifold. Four distinct regions are chosen in the manifold corresponding to the four phases of HIFU treatment (before HIFU treatment, during HIFU treatment, immediately after HIFU treatment and 10-min after HIFU treatment). It was found that disorganization of the points is achieved by increasing the acoustic power, and if the thermal lesion has been formed, the regions of points related to pre- and post-HIFU significantly differ. Moreover, the manifold embedding was repeated on 2-D moving windows in RF data envelopes related to pre- and post-HIFU exposure data frames. It was concluded that if mean values of the points related to pre- and post-exposure frames in the reconstructed manifold are estimated, and if the Euclidean distance between these two mean values is calculated and the sliding window is moved and this procedure is repeated for the whole image, a new image based on the Euclidean distance can be formed in which the HIFU thermal lesion is detectable.
Institute of Scientific and Technical Information of China (English)
高小方; 梁吉业
2013-01-01
流形学习已经成为机器学习与数据挖掘领域中一个重要的研究课题.目前的流形学习算法都假设所研究的高维数据存在于同一个流形上,并不能支持或者应用于大量存在的采样于多流形上的高维数据.针对等维度的独立多流形DC-ISOMAP算法,首先通过从采样密集点开始扩展切空间的方法将多流形准确分解为单个流形,并逐个计算其低维嵌入,然后基于各子流形间的内部位置关系将其低维嵌入组合起来,得到最终的嵌入结果.实验结果表明,该算法在人造数据和实际的人脸图像数据上都能有效地计算出高维数据的低维嵌入结果.%Manifold learning has become a hot issue in the field of machine learning and data mining.Its algorithms often assume that the data resides on a single manifold.And both the theories and algorithms are lacking when the data is supported on a mixture of manifolds.A new method,which is called DC-ISOMAP method,is proposed for the nonlinear dimensionality reduction of data lying on the separated multi-manifold with same intrinsic dimension.Although several algorithms based on spectral clustering or manifold clustering can separate sub-manifolds and get their low-dimensional embeddings,the algorithms do not think about the topological structure of multi-manifolds and must know the number of the clustered sub-manifolds.DC-ISOMAP firstly decomposes a given data set into several sub-manifolds by propagating the tangent subspace of the point with maximum sampling density to a separate sub-manifold,and then the low-dimensional embeddings of each sub-manifold is independently calculated.Finally the embeddings of all sub-manifolds are composed into their proper positions and orientations based on their inter-connections.Experimental results on synthetic data as well as real world images demonstrate that our approaches can construct an accurate low-dimensional representation of the data in an efficient manner.
Overview of manifold learning techniques for the investigation of disruptions on JET
Cannas, B.; Fanni, A.; Murari, A.; Pau, A.; Sias, G.; EFDA Contributors, JET
2014-11-01
Identifying a low-dimensional embedding of a high-dimensional data set allows exploration of the data structure. In this paper we tested some existing manifold learning techniques for discovering such embedding within the multidimensional operational space of a nuclear fusion tokamak. Among the manifold learning methods, the following approaches have been investigated: linear methods, such as principal component analysis and grand tour, and nonlinear methods, such as self-organizing map and its probabilistic variant, generative topographic mapping. In particular, the last two methods allow us to obtain a low-dimensional (typically two-dimensional) map of the high-dimensional operational space of the tokamak. These maps provide a way of visualizing the structure of the high-dimensional plasma parameter space and allow discrimination between regions characterized by a high risk of disruption and those with a low risk of disruption. The data for this study comes from plasma discharges selected from 2005 and up to 2009 at JET. The self-organizing map and generative topographic mapping provide the most benefits in the visualization of very large and high-dimensional datasets. Some measures have been used to evaluate their performance. Special emphasis has been put on the position of outliers and extreme points, map composition, quantization errors and topological errors.
Liu, Yang; Liu, Yan; Chan, Keith C C; Hua, Kien A
2014-12-01
In this brief, we present a novel supervised manifold learning framework dubbed hybrid manifold embedding (HyME). Unlike most of the existing supervised manifold learning algorithms that give linear explicit mapping functions, the HyME aims to provide a more general nonlinear explicit mapping function by performing a two-layer learning procedure. In the first layer, a new clustering strategy called geodesic clustering is proposed to divide the original data set into several subsets with minimum nonlinearity. In the second layer, a supervised dimensionality reduction scheme called locally conjugate discriminant projection is performed on each subset for maximizing the discriminant information and minimizing the dimension redundancy simultaneously in the reduced low-dimensional space. By integrating these two layers in a unified mapping function, a supervised manifold embedding framework is established to describe both global and local manifold structure as well as to preserve the discriminative ability in the learned subspace. Experiments on various data sets validate the effectiveness of the proposed method.
Multimodal manifold-regularized transfer learning for MCI conversion prediction.
Cheng, Bo; Liu, Mingxia; Suk, Heung-Il; Shen, Dinggang; Zhang, Daoqiang
2015-12-01
As the early stage of Alzheimer's disease (AD), mild cognitive impairment (MCI) has high chance to convert to AD. Effective prediction of such conversion from MCI to AD is of great importance for early diagnosis of AD and also for evaluating AD risk pre-symptomatically. Unlike most previous methods that used only the samples from a target domain to train a classifier, in this paper, we propose a novel multimodal manifold-regularized transfer learning (M2TL) method that jointly utilizes samples from another domain (e.g., AD vs. normal controls (NC)) as well as unlabeled samples to boost the performance of the MCI conversion prediction. Specifically, the proposed M2TL method includes two key components. The first one is a kernel-based maximum mean discrepancy criterion, which helps eliminate the potential negative effect induced by the distributional difference between the auxiliary domain (i.e., AD and NC) and the target domain (i.e., MCI converters (MCI-C) and MCI non-converters (MCI-NC)). The second one is a semi-supervised multimodal manifold-regularized least squares classification method, where the target-domain samples, the auxiliary-domain samples, and the unlabeled samples can be jointly used for training our classifier. Furthermore, with the integration of a group sparsity constraint into our objective function, the proposed M2TL has a capability of selecting the informative samples to build a robust classifier. Experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database validate the effectiveness of the proposed method by significantly improving the classification accuracy of 80.1 % for MCI conversion prediction, and also outperforming the state-of-the-art methods.
On the design of suboptimal sliding manifold for a class of nonlinear uncertain time-delay systems
Batmani, Yazdan; Khaloozadeh, Hamid
2016-08-01
This paper proposes a new method to design suboptimal sliding manifolds for a class of nonlinear uncertain systems with state and input delays. A switching control law is obtained based on the designed suboptimal sliding manifold. It is proved that the proposed method is able to guarantee the stability of the closed-loop system in the presence of uncertainty. Three numerical simulations are given to illustrate the effectiveness of the proposed method.
Chen, Xiaoguang; Liu, Dan; Xu, Guanghua; Jiang, Kuosheng; Liang, Lin
2014-12-26
For decades, bearing factory quality evaluation has been a key problem and the methods used are always static tests. This paper investigates the use of piezoelectric ultrasonic transducers (PUT) as dynamic diagnostic tools and a relevant signal classification technique, wavelet packet entropy (WPEntropy) flow manifold learning, for the evaluation of bearing factory quality. The data were analyzed using wavelet packet entropy (WPEntropy) flow manifold learning. The results showed that the ultrasonic technique with WPEntropy flow manifold learning was able to detect different types of defects on the bearing components. The test method and the proposed technique are described and the different signals are analyzed and discussed.
Using manifold learning for atlas selection in multi-atlas segmentation.
Directory of Open Access Journals (Sweden)
Albert K Hoang Duc
Full Text Available Multi-atlas segmentation has been widely used to segment various anatomical structures. The success of this technique partly relies on the selection of atlases that are best mapped to a new target image after registration. Recently, manifold learning has been proposed as a method for atlas selection. Each manifold learning technique seeks to optimize a unique objective function. Therefore, different techniques produce different embeddings even when applied to the same data set. Previous studies used a single technique in their method and gave no reason for the choice of the manifold learning technique employed nor the theoretical grounds for the choice of the manifold parameters. In this study, we compare side-by-side the results given by 3 manifold learning techniques (Isomap, Laplacian Eigenmaps and Locally Linear Embedding on the same data set. We assess the ability of those 3 different techniques to select the best atlases to combine in the framework of multi-atlas segmentation. First, a leave-one-out experiment is used to optimize our method on a set of 110 manually segmented atlases of hippocampi and find the manifold learning technique and associated manifold parameters that give the best segmentation accuracy. Then, the optimal parameters are used to automatically segment 30 subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI. For our dataset, the selection of atlases with Locally Linear Embedding gives the best results. Our findings show that selection of atlases with manifold learning leads to segmentation accuracy close to or significantly higher than the state-of-the-art method and that accuracy can be increased by fine tuning the manifold learning process.
Using manifold learning for atlas selection in multi-atlas segmentation.
Hoang Duc, Albert K; Modat, Marc; Leung, Kelvin K; Cardoso, M Jorge; Barnes, Josephine; Kadir, Timor; Ourselin, Sébastien
2013-01-01
Multi-atlas segmentation has been widely used to segment various anatomical structures. The success of this technique partly relies on the selection of atlases that are best mapped to a new target image after registration. Recently, manifold learning has been proposed as a method for atlas selection. Each manifold learning technique seeks to optimize a unique objective function. Therefore, different techniques produce different embeddings even when applied to the same data set. Previous studies used a single technique in their method and gave no reason for the choice of the manifold learning technique employed nor the theoretical grounds for the choice of the manifold parameters. In this study, we compare side-by-side the results given by 3 manifold learning techniques (Isomap, Laplacian Eigenmaps and Locally Linear Embedding) on the same data set. We assess the ability of those 3 different techniques to select the best atlases to combine in the framework of multi-atlas segmentation. First, a leave-one-out experiment is used to optimize our method on a set of 110 manually segmented atlases of hippocampi and find the manifold learning technique and associated manifold parameters that give the best segmentation accuracy. Then, the optimal parameters are used to automatically segment 30 subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). For our dataset, the selection of atlases with Locally Linear Embedding gives the best results. Our findings show that selection of atlases with manifold learning leads to segmentation accuracy close to or significantly higher than the state-of-the-art method and that accuracy can be increased by fine tuning the manifold learning process.
Institute of Scientific and Technical Information of China (English)
张振跃; 查宏远
2004-01-01
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
Olson, C. C.; Doster, T.
2016-05-01
We investigate the parameters that govern an unsupervised anomaly detection framework that uses nonlinear techniques to learn a better model of the non-anomalous data. A manifold or kernel-based model is learned from a small, uniformly sampled subset in order to reduce computational burden and under the assumption that anomalous data will have little effect on the learned model because their rarity reduces the likelihood of their inclusion in the subset. The remaining data are then projected into the learned space and their projection errors used as detection statistics. Here, kernel principal component analysis is considered for learning the background model. We consider spectral data from an 8-band multispectral sensor as well as panchromatic infrared images treated by building a data set composed of overlapping image patches. We consider detection performance as a function of patch neighborhood size as well as embedding parameters such as kernel bandwidth and dimension. ROC curves are generated over a range of parameters and compared to RX performance.
Deep Manifold Learning Combined With Convolutional Neural Networks for Action Recognition.
Chen, Xin; Weng, Jian; Lu, Wei; Xu, Jiaming; Weng, Jiasi
2017-09-15
Learning deep representations have been applied in action recognition widely. However, there have been a few investigations on how to utilize the structural manifold information among different action videos to enhance the recognition accuracy and efficiency. In this paper, we propose to incorporate the manifold of training samples into deep learning, which is defined as deep manifold learning (DML). The proposed DML framework can be adapted to most existing deep networks to learn more discriminative features for action recognition. When applied to a convolutional neural network, DML embeds the previous convolutional layer's manifold into the next convolutional layer; thus, the discriminative capacity of the next layer can be promoted. We also apply the DML on a restricted Boltzmann machine, which can alleviate the overfitting problem. Experimental results on four standard action databases (i.e., UCF101, HMDB51, KTH, and UCF sports) show that the proposed method outperforms the state-of-the-art methods.
Facial Expression Recognition of Various Internal States via Manifold Learning
Institute of Scientific and Technical Information of China (English)
Young-Suk Shin
2009-01-01
Emotions are becoming increasingly important in human-centered interaction architectures. Recognition of facial expressions, which are central to human-computer interactions, seems natural and desirable. However, facial expressions include mixed emotions, continuous rather than discrete, which vary from moment to moment. This paper represents a novel method of recognizing facial expressions of various internal states via manifold learning, to achieve the aim of humancentered interaction studies. A critical review of widely used emotion models is described, then, facial expression features of various internal states via the locally linear embedding (LLE) are extracted. The recognition of facial expressions is created with the pleasure-displeasure and arousal-sleep dimensions in a two-dimensional model of emotion. The recognition result of various internal state expressions that mapped to the embedding space via the LLE algorithm can effectively represent the structural nature of the two-dimensional model of emotion. Therefore our research has established that the relationship between facial expressions of various internal states can be elaborated in the two-dimensional model of emotion, via the locally linear embedding algorithm.
Descriptor Learning via Supervised Manifold Regularization for Multioutput Regression.
Zhen, Xiantong; Yu, Mengyang; Islam, Ali; Bhaduri, Mousumi; Chan, Ian; Li, Shuo
2016-06-08
Multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis. However, due to the huge image variability and ambiguity, it is fundamentally challenging to handle the highly complex input-target relationship of multioutput regression, especially with indiscriminate high-dimensional representations. In this paper, we propose a novel supervised descriptor learning (SDL) algorithm for multioutput regression, which can establish discriminative and compact feature representations to improve the multivariate estimation performance. The SDL is formulated as generalized low-rank approximations of matrices with a supervised manifold regularization. The SDL is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low-dimensional space aligned to targets. The achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression, which enables more accurate and efficient multivariate estimation. We conduct extensive evaluation of the proposed SDL on both synthetic data and real-world multioutput regression tasks for both computer vision and medical image analysis. Experimental results have shown that the proposed SDL can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts. Our method establishes a novel SDL framework for multioutput regression, which can be widely used to boost the performance in different applications.
Xie, Xiaofeng; Yu, Zhu Liang; Lu, Haiping; Gu, Zhenghui; Li, Yuanqing
2016-07-07
In motor imagery brain-computer interfaces (BCIs), the symmetric positive-definite (SPD) covariance matrices of electroencephalogram (EEG) signals carry important discriminative information. In this paper, we intend to classify motor imagery EEG signals by exploiting the fact that the space of SPD matrices endowed with Riemannian distance is a highdimensional Riemannian manifold. To alleviate the overfitting and heavy computation problems associated with conventional classification methods on high-dimensional manifold, we propose a framework for intrinsic sub-manifold learning from a high-dimensional Riemannian manifold. Considering a special case of SPD space, a simple yet efficient bilinear sub-manifold learning (BSML) algorithm is derived to learn the intrinsic submanifold by identifying a bilinear mapping that maximizes the preservation of the local geometry and global structure of the original manifold. Two BSML-based classification algorithms are further proposed to classify the data on a learned intrinsic sub-manifold. Experimental evaluation of the classification of EEG revealed that the BSML method extracts the intrinsic submanifold approximately 5 faster and with higher classification accuracy compared with competing algorithms. The BSML also exhibited strong robustness against a small training dataset, which often occurs in BCI studies.
Building robust neighborhoods for manifold learning-based image classification and anomaly detection
Doster, Timothy; Olson, Colin C.
2016-05-01
We exploit manifold learning algorithms to perform image classification and anomaly detection in complex scenes involving hyperspectral land cover and broadband IR maritime data. The results of standard manifold learning techniques are improved by including spatial information. This is accomplished by creating super-pixels which are robust to affine transformations inherent in natural scenes. We utilize techniques from harmonic analysis and image processing, namely, rotation, skew, flip, and shift operators to develop a more representational graph structure which defines the data-dependent manifold.
Supervised learning for neural manifold using spatiotemporal brain activity
Kuo, Po-Chih; Chen, Yong-Sheng; Chen, Li-Fen
2015-12-01
Objective. Determining the means by which perceived stimuli are compactly represented in the human brain is a difficult task. This study aimed to develop techniques for the construction of the neural manifold as a representation of visual stimuli. Approach. We propose a supervised locally linear embedding method to construct the embedded manifold from brain activity, taking into account similarities between corresponding stimuli. In our experiments, photographic portraits were used as visual stimuli and brain activity was calculated from magnetoencephalographic data using a source localization method. Main results. The results of 10 × 10-fold cross-validation revealed a strong correlation between manifolds of brain activity and the orientation of faces in the presented images, suggesting that high-level information related to image content can be revealed in the brain responses represented in the manifold. Significance. Our experiments demonstrate that the proposed method is applicable to investigation into the inherent patterns of brain activity.
Eslami, Abouzar; Yigitsoy, Mehmet; Navab, Nassir
2011-01-01
In this paper we propose a new method for shape guided segmentation of cardiac boundaries based on manifold learning of the shapes represented by the phase field approximation of the Mumford-Shah functional. A novel distance is defined to measure the similarity of shapes without requiring deformable registration. Cardiac motion is compensated and phases are mapped into one reference phase, that is the end of diastole, to avoid time warping and synchronization at all cardiac phases. Non-linear embedding of these 3D shapes extracts the manifold of the inter-subject variation of the heart shape to be used for guiding the segmentation for a new subject. For validation the method is applied to a comprehensive dataset of 3D+t cardiac Cine MRI from normal subjects and patients.
Acoustic space learning for sound-source separation and localization on binaural manifolds.
Deleforge, Antoine; Forbes, Florence; Horaud, Radu
2015-02-01
In this paper, we address the problems of modeling the acoustic space generated by a full-spectrum sound source and using the learned model for the localization and separation of multiple sources that simultaneously emit sparse-spectrum sounds. We lay theoretical and methodological grounds in order to introduce the binaural manifold paradigm. We perform an in-depth study of the latent low-dimensional structure of the high-dimensional interaural spectral data, based on a corpus recorded with a human-like audiomotor robot head. A nonlinear dimensionality reduction technique is used to show that these data lie on a two-dimensional (2D) smooth manifold parameterized by the motor states of the listener, or equivalently, the sound-source directions. We propose a probabilistic piecewise affine mapping model (PPAM) specifically designed to deal with high-dimensional data exhibiting an intrinsic piecewise linear structure. We derive a closed-form expectation-maximization (EM) procedure for estimating the model parameters, followed by Bayes inversion for obtaining the full posterior density function of a sound-source direction. We extend this solution to deal with missing data and redundancy in real-world spectrograms, and hence for 2D localization of natural sound sources such as speech. We further generalize the model to the challenging case of multiple sound sources and we propose a variational EM framework. The associated algorithm, referred to as variational EM for source separation and localization (VESSL) yields a Bayesian estimation of the 2D locations and time-frequency masks of all the sources. Comparisons of the proposed approach with several existing methods reveal that the combination of acoustic-space learning with Bayesian inference enables our method to outperform state-of-the-art methods.
Wang, Yi; Xu, Guanghua; Liang, Lin; Jiang, Kuosheng
2015-03-01
The kurtogram-based methods have been proved powerful and practical to detect and characterize transient components in a signal. The basic idea of the kurtogram-based methods is to use the kurtosis as a measure to discover the presence of transient impulse components and to indicate the frequency band where these occur. However, the performance of the kurtogram-based methods is poor due to the low signal-to-noise ratio. As the weak transient signal with a wide spread frequency band can be easily masked by noise. Besides, selecting signal just in one frequency band will leave out some transient features. Aiming at these shortcomings, different frequency bands signal fusion is adopted in this paper. Considering that manifold learning aims at discovering the nonlinear intrinsic structure which embedded in high dimensional data, this paper proposes a waveform feature manifold (WFM) method to extract the weak signature from waveform feature space which obtained by binary wavelet packet transform. Minimum permutation entropy is used to select the optimal parameter in a manifold learning algorithm. A simulated bearing fault signal and two real bearing fault signals are used to validate the improved performance of the proposed method through the comparison with the kurtogram-based methods. The results show that the proposed method outperforms the kurtogram-based methods and is effective in weak signature extraction.
Quantum filter reduction for measurement-feedback control via unsupervised manifold learning
DEFF Research Database (Denmark)
Nielsen, Anne Ersbak Bang; Hopkins, Asa S .; Mabuchi, Hideo
2009-01-01
We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space...
Manifold learning on brain functional networks in aging.
Qiu, Anqi; Lee, Annie; Tan, Mingzhen; Chung, Moo K
2015-02-01
We propose a new analysis framework to utilize the full information of brain functional networks for computing the mean of a set of brain functional networks and embedding brain functional networks into a low-dimensional space in which traditional regression and classification analyses can be easily employed. For this, we first represent the brain functional network by a symmetric positive matrix computed using sparse inverse covariance estimation. We then impose a Log-Euclidean Riemannian manifold structure on brain functional networks whose norm gives a convenient and practical way to define a mean. Finally, based on the fact that the computation of linear operations can be done in the tangent space of this Riemannian manifold, we adopt Locally Linear Embedding (LLE) to the Log-Euclidean Riemannian manifold space in order to embed the brain functional networks into a low-dimensional space. We show that the integration of the Log-Euclidean manifold with LLE provides more efficient and succinct representation of the functional network and facilitates regression analysis, such as ridge regression, on the brain functional network to more accurately predict age when compared to that of the Euclidean space of functional networks with LLE. Interestingly, using the Log-Euclidean analysis framework, we demonstrate the integration and segregation of cortical-subcortical networks as well as among the salience, executive, and emotional networks across lifespan.
Spectral Target Detection using Physics-Based Modeling and a Manifold Learning Technique
Albano, James A.
Identification of materials from calibrated radiance data collected by an airborne imaging spectrometer depends strongly on the atmospheric and illumination conditions at the time of collection. This thesis demonstrates a methodology for identifying material spectra using the assumption that each unique material class forms a lower-dimensional manifold (surface) in the higher-dimensional spectral radiance space and that all image spectra reside on, or near, these theoretic manifolds. Using a physical model, a manifold characteristic of the target material exposed to varying illumination and atmospheric conditions is formed. A graph-based model is then applied to the radiance data to capture the intricate structure of each material manifold, followed by the application of the commute time distance (CTD) transformation to separate the target manifold from the background. Detection algorithms are then applied in the CTD subspace. This nonlinear transformation is based on a random walk on a graph and is derived from an eigendecomposition of the pseudoinverse of the graph Laplacian matrix. This work provides a geometric interpretation of the CTD transformation, its algebraic properties, the atmospheric and illumination parameters varied in the physics-based model, and the influence the target manifold samples have on the orientation of the coordinate axes in the transformed space. This thesis concludes by demonstrating improved detection results in the CTD subspace as compared to detection in the original spectral radiance space.
Spectral target detection using a physical model and a manifold learning technique
Albano, James A.; Messinger, David W.; Ientilucci, Emmett
2013-05-01
Identification of materials from calibrated radiance data collected by an airborne imaging spectrometer depends strongly on the atmospheric and illumination conditions at the time of collection. This paper presents a methodology for identifying material spectra using the assumption that each unique material class forms a lower-dimensional manifold (surface) in the higher-dimensional spectral radiance space and that all image spectra reside on, or near, these theoretic manifolds. Using a physical model, a manifold characteristic of the target material exposed to varying illumination and atmospheric conditions is formed. A graph-based model is then applied to the radiance data to capture the intricate structure of each material manifold followed by the application of the commute time distance (CTD) transformation to separate the target manifold from the background. Detection algorithms are than applied in the CTD subspace. This nonlinear transformation is based on a Markov-chain model of a random walk on a graph and is derived from an eigendecomposition of the pseudoinverse of the graph Laplacian matrix. This paper discusses the properties of the CTDtransformation, the atmospheric and illumination parameters varied in the physics-based model and demonstrates the influence the target manifold samples have on the orientation of the coordinate axes in the transformed space. A comparison between detection performance in the CTD subspace and spectral radiance space is also given for two hyperspectral images.
Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning.
Peng, Yong; Lu, Bao-Liang; Wang, Suhang
2015-05-01
Constructing an informative and discriminative graph plays an important role in various pattern recognition tasks such as clustering and classification. Among the existing graph-based learning models, low-rank representation (LRR) is a very competitive one, which has been extensively employed in spectral clustering and semi-supervised learning (SSL). In SSL, the graph is composed of both labeled and unlabeled samples, where the edge weights are calculated based on the LRR coefficients. However, most of existing LRR related approaches fail to consider the geometrical structure of data, which has been shown beneficial for discriminative tasks. In this paper, we propose an enhanced LRR via sparse manifold adaption, termed manifold low-rank representation (MLRR), to learn low-rank data representation. MLRR can explicitly take the data local manifold structure into consideration, which can be identified by the geometric sparsity idea; specifically, the local tangent space of each data point was sought by solving a sparse representation objective. Therefore, the graph to depict the relationship of data points can be built once the manifold information is obtained. We incorporate a regularizer into LRR to make the learned coefficients preserve the geometric constraints revealed in the data space. As a result, MLRR combines both the global information emphasized by low-rank property and the local information emphasized by the identified manifold structure. Extensive experimental results on semi-supervised classification tasks demonstrate that MLRR is an excellent method in comparison with several state-of-the-art graph construction approaches.
Fault diagnosis model based on multi-manifold learning and PSO-SVM for machinery
Institute of Scientific and Technical Information of China (English)
Wang Hongjun; Xu Xiaoli; Rosen B G
2014-01-01
Fault diagnosis technology plays an important role in the industries due to the emergency fault of a machine could bring the heavy lost for the people and the company. A fault diagnosis model based on multi-manifold learning and particle swarm optimization support vector machine (PSO-SVM) is studied. This fault diagnosis model is used for a rolling bearing experimental of three kinds faults. The results are verified that this model based on multi-manifold learning and PSO-SVM is good at the fault sensitive features acquisition with effective accuracy.
Non-rigid registration of medical images based on ordinal feature and manifold learning
Li, Qi; Liu, Jin; Zang, Bo
2015-12-01
With the rapid development of medical imaging technology, medical image research and application has become a research hotspot. This paper offers a solution to non-rigid registration of medical images based on ordinal feature (OF) and manifold learning. The structural features of medical images are extracted by combining ordinal features with local linear embedding (LLE) to improve the precision and speed of the registration algorithm. A physical model based on manifold learning and optimization search is constructed according to the complicated characteristics of non-rigid registration. The experimental results demonstrate the robustness and applicability of the proposed registration scheme.
Manifold regularized multitask learning for semi-supervised multilabel image classification.
Luo, Yong; Tao, Dacheng; Geng, Bo; Xu, Chao; Maybank, Stephen J
2013-02-01
It is a significant challenge to classify images with multiple labels by using only a small number of labeled samples. One option is to learn a binary classifier for each label and use manifold regularization to improve the classification performance by exploring the underlying geometric structure of the data distribution. However, such an approach does not perform well in practice when images from multiple concepts are represented by high-dimensional visual features. Thus, manifold regularization is insufficient to control the model complexity. In this paper, we propose a manifold regularized multitask learning (MRMTL) algorithm. MRMTL learns a discriminative subspace shared by multiple classification tasks by exploiting the common structure of these tasks. It effectively controls the model complexity because different tasks limit one another's search volume, and the manifold regularization ensures that the functions in the shared hypothesis space are smooth along the data manifold. We conduct extensive experiments, on the PASCAL VOC'07 dataset with 20 classes and the MIR dataset with 38 classes, by comparing MRMTL with popular image classification algorithms. The results suggest that MRMTL is effective for image classification.
An adaptive locally linear embedding manifold learning approach for hyperspectral target detection
Ziemann, Amanda K.; Messinger, David W.
2015-05-01
Algorithms for spectral analysis commonly use parametric or linear models of the data. Research has shown, however, that hyperspectral data -- particularly in materially cluttered scenes -- are not always well-modeled by statistical or linear methods. Here, we propose an approach to hyperspectral target detection that is based on a graph theory model of the data and a manifold learning transformation. An adaptive nearest neighbor (ANN) graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation. The artificial target manifold helps to guide the separation of the target data from the background data in the new, transformed manifold coordinates. Then, target detection is performed in the manifold space using Spectral Angle Mapper. This methodology is an improvement over previous iterations of this approach due to the incorporation of ANN, the artificial target manifold, and the choice of detector in the transformed space. We implement our approach in a spatially local way: the image is delineated into square tiles, and the detection maps are normalized across the entire image. Target detection results will be shown using laboratory-measured and scene-derived target data from the SHARE 2012 collect.
Laplacian Eigenmaps manifold learning for landmark localization in brain MR images.
Guerrero, Ricardo; Wolz, Robin; Rueckert, Daniel
2011-01-01
The identification of anatomical landmarks in medical images is an important task in registration and morphometry. Manual labeling is time consuming and prone to observer errors. We propose a manifold learning procedure, based on Laplacian Eigenmaps, that learns an embedding from patches drawn from multiple brain MR images. The position of the patches in the manifold can be used to predict the location of the landmarks via regression. New images are embedded in the manifold and the resulting coordinates are used to predict the landmark position in the new image. The output of multiple regressors is fused in a weighted fashion to boost the accuracy and robustness. We demonstrate this framework in 3D brain MR images from the ADNI database. We show an accuracy of -0.5mm, an increase of at least two fold when compared to traditional approaches such as registration or sliding windows.
Parts-based stereoscopic image assessment by learning binocular manifold color visual properties
Xu, Haiyong; Yu, Mei; Luo, Ting; Zhang, Yun; Jiang, Gangyi
2016-11-01
Existing stereoscopic image quality assessment (SIQA) methods are mostly based on the luminance information, in which color information is not sufficiently considered. Actually, color is part of the important factors that affect human visual perception, and nonnegative matrix factorization (NMF) and manifold learning are in line with human visual perception. We propose an SIQA method based on learning binocular manifold color visual properties. To be more specific, in the training phase, a feature detector is created based on NMF with manifold regularization by considering color information, which not only allows parts-based manifold representation of an image, but also manifests localized color visual properties. In the quality estimation phase, visually important regions are selected by considering different human visual attention, and feature vectors are extracted by using the feature detector. Then the feature similarity index is calculated and the parts-based manifold color feature energy (PMCFE) for each view is defined based on the color feature vectors. The final quality score is obtained by considering a binocular combination based on PMCFE. The experimental results on LIVE I and LIVE Π 3-D IQA databases demonstrate that the proposed method can achieve much higher consistency with subjective evaluations than the state-of-the-art SIQA methods.
Modern Multivariate Statistical Techniques Regression, Classification, and Manifold Learning
Izenman, Alan Julian
2006-01-01
Describes the advances in computation and data storage that led to the introduction of many statistical tools for high-dimensional data analysis. Focusing on multivariate analysis, this book discusses nonlinear methods as well as linear methods. It presents an integrated mixture of classical and modern multivariate statistical techniques.
Isospectral Manifold Learning Algorithm%等谱流形学习算法
Institute of Scientific and Technical Information of China (English)
黄运娟; 李凡长
2013-01-01
基于谱方法的流形学习算法的目标是发现嵌入在高维数据空间中的低维表示。近年来,该算法已得到广泛的应用。等谱流形学习是谱方法中的主要内容之一。等谱流形学习源于这样的结论：只要两个流形的谱相同,其内部结构就是相同的。而谱计算难以解决的问题是近邻参数的选择以及如何构造合理邻接权。为此,提出了等谱流形学习算法(isospectral manifold learning algorithm,简称IMLA)。它通过直接修正稀疏重构权矩阵,将类内的判别监督信息和类间的判别监督信息同时融入邻接图,达到既能保持数据间稀疏重建关系,又能利用监督信息的目的,与 PCA等算法相比具有明显的优势。该算法在3个常用人脸数据集(Yale,ORL,Extended Yale B)上得到了验证,这进一步说明了IMLA算法的有效性。%Manifold learning based on spectral method has been widely used recently for discovering a low-dimensional representation in the high-dimensional vector space. Isospectral manifold learning is one of the main contents of spectrum method. Isospectral manifold learning stems from the conclusions that if only the spectrums of manifold are the same, so are their internal structures. However, the difficult task about the calculation of the spectrum is how to select the optimal neighborhood size and construct reasonable neighboring weights. In this paper, a supervised technique called isospectral manifold learning algorithm (IMLA) is proposed. By modifying directly sparse reconstruction weight, IMLA takes into account the within-neighboring information and between-neighboring information. Thus, it not only preserves the sparse reconstructive relationship, but also sufficiently utilizes discriminant information. Compared with PCA and other algorithms, IMLA has obvious advantages. Experimental results on face databases (Yale, ORL and Extended Yale B) show the effectiveness of the IMLA method.
A hybrid manifold learning algorithm for the diagnosis and prognostication of Alzheimer's disease.
Dai, Peng; Gwadry-Sridhar, Femida; Bauer, Michael; Borrie, Michael
The diagnosis of Alzheimer's disease (AD) requires a variety of medical tests, which leads to huge amounts of multivariate heterogeneous data. Such data are difficult to compare, visualize, and analyze due to the heterogeneous nature of medical tests. We present a hybrid manifold learning framework, which embeds the feature vectors in a subspace preserving the underlying pairwise similarity structure, i.e. similar/dissimilar pairs. Evaluation tests are carried out using the neuroimaging and biological data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) in a three-class (normal, mild cognitive impairment, and AD) classification task using support vector machine (SVM). Furthermore, we make extensive comparison with standard manifold learning algorithms, such as Principal Component Analysis (PCA), Principal Component Analysis (PCA), Multidimensional Scaling (MDS), and isometric feature mapping (Isomap). Experimental results show that our proposed algorithm yields an overall accuracy of 85.33% in the three-class task.
Manifold learning for atlas selection in multi-atlas-based segmentation of hippocampus
Hoang Duc, Albert K.; Modat, Marc; Leung, Kelvin K.; Kadir, Timor; Ourselin, Sébastien
2012-02-01
Alzheimer's disease (AD) severely affects the hippocampus: it loses mass and shrinks as the disease advances. Thus delineation of the hippocampus is an important task in the clinical study of AD. Because of its simplicity and good performance, multi-atlas based segmentation has become a popular approach for medical image segmentation. We propose to use manifold learning for atlas selection in the framework of multi-atlas based segmentation. The framework only benefits when selecting atlases similar to the target image. Since manifold learning assigns each image a coordinate in low-dimensional space by respecting the neighborhood relationship, it is well suited for atlas selection. The key contribution is that we use manifold learning based on a metric derived from non-rigid transformation as the resulting embedding better captures deformations or shape differences between images than similarity measures based on voxel intensity. The proposed method is evaluated in a leave-one-out experiment on a set of 110 hippocampus images; we report mean Dice score of 0.9114 (0.0227). The method was validated against a state-of-the-art method for hippocampus segmentation.
Manifold learning for image-based breathing gating with application to 4D ultrasound.
Wachinger, Christian; Yigitsoy, Mehmet; Navab, Nassir
2010-01-01
Breathing motion leads to a significant displacement and deformation of organs in the abdominal region. This makes the detection of the breathing phase for numerous applications necessary. We propose a new, purely image-based respiratory gating method for ultrasound. Further, we use this technique to provide a solution for breathing affected 4D ultrasound acquisitions with a wobbler probe. We achieve the gating with Laplacian eigenmaps, a manifold learning technique, to determine the low-dimensional manifold embedded in the high-dimensional image space. Since Laplacian eigenmaps assign each ultrasound frame a coordinate in low-dimensional space by respecting the neighborhood relationship, they are well suited for analyzing the breathing cycle. For the 4D application, we perform the manifold learning for each angle, and consecutively, align all the local curves and perform a curve fitting to achieve a globally consistent breathing signal. We performed the image-based gating on several 2D and 3D ultrasound datasets over time, and quantified its very good performance by comparing it to measurements from an external gating system.
Manifold learning for image-based breathing gating in ultrasound and MRI.
Wachinger, Christian; Yigitsoy, Mehmet; Rijkhorst, Erik-Jan; Navab, Nassir
2012-05-01
Respiratory motion is a challenging factor for image acquisition and image-guided procedures in the abdominal and thoracic region. In order to address the issues arising from respiratory motion, it is often necessary to detect the respiratory signal. In this article, we propose a novel, purely image-based retrospective respiratory gating method for ultrasound and MRI. Further, we apply this technique to acquire breathing-affected 4D ultrasound with a wobbler probe and, similarly, to create 4D MR with a slice stacking approach. We achieve the gating with Laplacian eigenmaps, a manifold learning technique, to determine the low-dimensional manifold embedded in the high-dimensional image space. Since Laplacian eigenmaps assign to each image frame a coordinate in low-dimensional space by respecting the neighborhood relationship, they are well suited for analyzing the breathing cycle. We perform the image-based gating on several 2D and 3D ultrasound datasets over time, and quantify its very good performance by comparing it to measurements from an external gating system. For MRI, we perform the manifold learning on several datasets for various orientations and positions. We achieve very high correlations by a comparison to an alternative gating with diaphragm tracking.
Xing, Fuyong; Yang, Lin
2015-10-01
Efficient and effective cell segmentation of neuroendocrine tumor (NET) in whole slide scanned images is a difficult task due to a large number of cells. The weak or misleading cell boundaries also present significant challenges. In this paper, we propose a fast, high throughput cell segmentation algorithm by combining top-down shape models and bottom-up image appearance information. A scalable sparse manifold learning method is proposed to model multiple subpopulations of different cell shape priors. Followed by a shape clustering on the manifold, a novel affine transform-approximated active contour model is derived to deform contours without solving a large amount of computationally-expensive Euler-Lagrange equations, and thus dramatically reduces the computational time. To the best of our knowledge, this is the first report of a high throughput cell segmentation algorithm for whole slide scanned pathology specimens using manifold learning to accelerate active contour models. The proposed approach is tested using 12 NET images, and the comparative experiments with the state of the arts demonstrate its superior performance in terms of both efficiency and effectiveness.
A machine learning approach to nonlinear modal analysis
Worden, K.; Green, P. L.
2017-02-01
Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, its extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw-Pierre approach is rather demanding technically, depending as it does on the analytical construction of a mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach motivated by Shaw-Pierre method which exploits the idea of statistical independence to optimise a parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD). A machine learning approach to inversion of the modal transformation is presented, based on the use of Gaussian processes, and this is equivalent to a nonlinear form of modal superposition. However, it is shown that issues can arise if the forward transformation is a polynomial and can thus have a multi-valued inverse. The overall approach is demonstrated using a number of case studies based on both simulated and experimental data.
A study on neural learning on manifold foliations: the case of the Lie group SU(3).
Fiori, Simone
2008-04-01
Learning on differential manifolds may involve the optimization of a function of many parameters. In this letter, we deal with Riemannian-gradient-based optimization on a Lie group, namely, the group of unitary unimodular matrices SU(3). In this special case, subalgebras of the associated Lie algebra su(3) may be individuated by computing pair-wise Gell-Mann matrices commutators. Subalgebras generate subgroups of a Lie group, as well as manifold foliation. We show that the Riemannian gradient may be projected over tangent structures to foliation, giving rise to foliation gradients. Exponentiations of foliation gradients may be computed in closed forms, which closely resemble Rodriguez forms for the special orthogonal group SO(3). We thus compare optimization by Riemannian gradient and foliation gradients.
流形学习在机械故障诊断中的应用研究%An Investigation of Applying Manifold Learning to Diagnose Machinery Faults
Institute of Scientific and Technical Information of China (English)
王冠伟; 张春霞; 庄健; 于德弘
2012-01-01
本文针对信号采集系统的特性对流形学习方法性能的影响尚不明确这一问题,采用理论分析和模拟实验的方法,研究了信号采样系统的非线性、零点漂移等特性对流形学习算法性能的影响.结果表明,当信号采样系统的特性保持相对稳定时,流形学习方法可以在一定程度上容忍系统存在的非线性和零点漂移效应.为了使流形学习算法达到较好的效果,在数据的搜集和预处理过程中,应使得数据容易重构到一个高维空间中且它们之间的相似性易于度量.从而,本文的研究结果为流形学习方法在机械故障诊断中的应用提供了一定的理论基础.%Currently, it is still not clear how the characteristics of a signal sampling system affect the performance of a manifold learning technique. This paper investigates the influence of the nonlinearity and zero-drift of a signal sampling system on the performance of a manifold learning technique theoretically and experimentally. Based on the obtained results, the following conclusions can be yielded. When the characteristics of the signal sampling system maintain stable relatively, manifold learning can tolerate the existence of systemic nonlinearity and zero-offset effect to a certain extent. In order to make a manifold learning algorithm achieve good performance, it requires that the collected data should be easily reconstructed into a high-dimensional space and the dissimilarity between them can be reasonably measured. Therefore, the research results in this paper lay a theoretical foundation to the application of manifold learning methods in machinery fault diagnosis.
A manifold learning method to detect respiratory signal from liver ultrasound images.
Wu, Jiaze; Gogna, Apoorva; Tan, Bien Soo; Ooi, London Lucien; Tian, Qi; Liu, Feng; Liu, Jimin
2015-03-01
Respiratory gating has been widely applied for respiratory correction or compensation in image acquisition and image-guided interventions. A novel image-based method is proposed to extract respiratory signal directly from 2D ultrasound liver images. The proposed method utilizes a typical manifold learning method, based on local tangent space alignment based technique, to detect principal respiratory motion from a sequence of ultrasound images. This technique assumes all the images lying on a low-dimensional manifold embedding into the high-dimensional image space, constructs an approximate tangent space of each point to represent its local geometry on the manifold, and then aligns the local tangent spaces to form the global coordinate system, where the respiratory signal is extracted. The experimental results show that the proposed method can detect relatively accurate respiratory signal with high correlation coefficient (0.9775) with respect to the ground-truth signal by tracking external markers, and achieve satisfactory computing performance (2.3s for an image sequence of 256 frames). The proposed method is also used to create breathing-corrected 3D ultrasound images to demonstrate its potential application values.
Learning Expressionlets via Universal Manifold Model for Dynamic Facial Expression Recognition
Liu, Mengyi; Shan, Shiguang; Wang, Ruiping; Chen, Xilin
2016-12-01
Facial expression is temporally dynamic event which can be decomposed into a set of muscle motions occurring in different facial regions over various time intervals. For dynamic expression recognition, two key issues, temporal alignment and semantics-aware dynamic representation, must be taken into account. In this paper, we attempt to solve both problems via manifold modeling of videos based on a novel mid-level representation, i.e. \\textbf{expressionlet}. Specifically, our method contains three key stages: 1) each expression video clip is characterized as a spatial-temporal manifold (STM) formed by dense low-level features; 2) a Universal Manifold Model (UMM) is learned over all low-level features and represented as a set of local modes to statistically unify all the STMs. 3) the local modes on each STM can be instantiated by fitting to UMM, and the corresponding expressionlet is constructed by modeling the variations in each local mode. With above strategy, expression videos are naturally aligned both spatially and temporally. To enhance the discriminative power, the expressionlet-based STM representation is further processed with discriminant embedding. Our method is evaluated on four public expression databases, CK+, MMI, Oulu-CASIA, and FERA. In all cases, our method outperforms the known state-of-the-art by a large margin.
流形学习及其算法研究%Manifold Learning and Research of Algorithm
Institute of Scientific and Technical Information of China (English)
闫志敏; 刘希玉
2011-01-01
Manifold learning is a branch of differential geometry, it will find embedded in high dimensional data in low dimensional manifold structure, which most of the algorithms are also used for dimensionality reduction, and some are also used for data visualization.Currently, Manifold learning gradually becomes a hotspot in the field of machine learning and pattern recognition. First, described the basic concepts of the manifold and manifold learning, then discussed the respective characteristics of manifold learning algorithms and analysed their shortcomings. You can use these algorithms better for data analysis and dimensionality reduction in the future of Manifold learning study.%流形学习作为微分几何的一个分支,旨在找出嵌入在高维数据中的低维流形结构,它的大部分算法都是用来进行维数约简的,也有一部分用来进行数据可视化的.目前,流形学习渐渐成为机器学习及模式识别领域中的一个研究热点.介绍了流形以及流形学习的基本概念,针对流形学习中的几种学习算法,讨论了它们各自的特点并分分析了它们的不足之处,以便在以后的流形学习研究中能够更好地运用这些算法对数据进行分析以及降维.
An empirical study on the performance of spectral manifold learning techniques
DEFF Research Database (Denmark)
Mysling, Peter; Hauberg, Søren; Pedersen, Kim Steenstrup
2011-01-01
as they are subjected to increasingly difficult problems. We evaluate performance in terms of both a classification and a regression task. Our study includes Isomap, LLE, Laplacian eigenmaps, and diffusion maps. Among others, our results indicate that the techniques are highly dependent on data density, sensitive......In recent years, there has been a surge of interest in spectral manifold learning techniques. Despite the interest, only little work has focused on the empirical behavior of these techniques. We construct synthetic data of variable complexity and observe the performance of the techniques...... to scaling, and greatly influenced by intrinsic dimensionality....
Sun, Jiaqi; Xie, Yuchen; Ye, Wenxing; Ho, Jeffrey; Entezari, Alireza; Blackband, Stephen J; Vemuri, Baba C
2013-01-01
In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are vectors in some Euclidean space, our dictionary learning algorithm is designed to incorporate the intrinsic geometric structure of manifolds and performs better than traditional dictionary learning approaches when applied to data lying on the manifold of square root densities. Non-negativity as well as smoothness across the whole field of the reconstructed DPs is guaranteed in our approach. We demonstrate the advantage of our approach by comparing it with an existing dictionary based reconstruction method on synthetic and real multi-shell MRI data.
Self-organized manifold learning and heuristic charting via adaptive metrics
Horvath, Denis; Brutovsky, Branislav
2014-01-01
Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However, their use is crucially limited to the cases when data are inherently reducible to low dimensionality. In general, drawbacks and limitations of these, as well as pure, MDS variants become more apparent when the exploration (learning) is exposed to the structured data of high intrinsic dimension. As we demonstrate on artificial and real-world datasets, the over-determination problem can be solved by means of the hybrid and multi-component discrete-continuous multi-modal optimization heuristics. Its remarkable feature is, that projections onto 2D are constructed simultaneously with the data categorization (classification) compensating in part for the loss of original input information. We observed, that the optimization module integrated with ML modeling, metric learning and categ...
Prediction of high-dimensional states subject to respiratory motion: a manifold learning approach
Liu, Wenyang; Sawant, Amit; Ruan, Dan
2016-07-01
The development of high-dimensional imaging systems in image-guided radiotherapy provides important pathways to the ultimate goal of real-time full volumetric motion monitoring. Effective motion management during radiation treatment usually requires prediction to account for system latency and extra signal/image processing time. It is challenging to predict high-dimensional respiratory motion due to the complexity of the motion pattern combined with the curse of dimensionality. Linear dimension reduction methods such as PCA have been used to construct a linear subspace from the high-dimensional data, followed by efficient predictions on the lower-dimensional subspace. In this study, we extend such rationale to a more general manifold and propose a framework for high-dimensional motion prediction with manifold learning, which allows one to learn more descriptive features compared to linear methods with comparable dimensions. Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where accurate and efficient prediction can be performed. A fixed-point iterative pre-image estimation method is used to recover the predicted value in the original state space. We evaluated and compared the proposed method with a PCA-based approach on level-set surfaces reconstructed from point clouds captured by a 3D photogrammetry system. The prediction accuracy was evaluated in terms of root-mean-squared-error. Our proposed method achieved consistent higher prediction accuracy (sub-millimeter) for both 200 ms and 600 ms lookahead lengths compared to the PCA-based approach, and the performance gain was statistically significant.
Aljabar, P; Wolz, R; Srinivasan, L; Counsell, S J; Rutherford, M A; Edwards, A D; Hajnal, J V; Rueckert, D
2011-12-01
Large medical image datasets form a rich source of anatomical descriptions for research into pathology and clinical biomarkers. Many features may be extracted from data such as MR images to provide, through manifold learning methods, new representations of the population's anatomy. However, the ability of any individual feature to fully capture all aspects morphology is limited. We propose a framework for deriving a representation from multiple features or measures which can be chosen to suit the application and are processed using separate manifold-learning steps. The results are then combined to give a single set of embedding coordinates for the data. We illustrate the framework in a population study of neonatal brain MR images and show how consistent representations, correlating well with clinical data, are given by measures of shape and of appearance. These particular measures were chosen as the developing neonatal brain undergoes rapid changes in shape and MR appearance and were derived from extracted cortical surfaces, nonrigid deformations, and image similarities. Combined single embeddings show improved correlations demonstrating their benefit for further studies such as identifying patterns in the trajectories of brain development. The results also suggest a lasting effect of age at birth on brain morphology, coinciding with previous clinical studies.
Face recognition based on subset selection via metric learning on manifold
Institute of Scientific and Technical Information of China (English)
Hong SHAO; Shuang CHEN; Jie-yi ZHAO; Wen-cheng CUI; Tian-shu YU
2015-01-01
With the development of face recognition using sparse representation based classifi cation (SRC), many relevant methods have been proposed and investigated. However, when the dictionary is large and the representation is sparse, only a small proportion of the elements contributes to the l1-minimization. Under this observation, several approaches have been developed to carry out an eﬃcient element selection procedure before SRC. In this paper, we employ a metric learning approach which helps fi nd the active elements correctly by taking into account the interclass/intraclass relationship and manifold structure of face images. After the metric has been learned, a neighborhood graph is constructed in the projected space. A fast marching algorithm is used to rapidly select the subset from the graph, and SRC is implemented for classifi cation. Experimental results show that our method achieves promising performance and signifi cant eﬃciency enhancement.
Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis
Shnitzer, Tal; Talmon, Ronen; Slotine, Jean-Jacques
2017-02-01
Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we propose a method for building an intrinsic representation of such signals in a purely data-driven manner. First, we apply a manifold learning technique, diffusion maps, to learn the intrinsic model of the latent variables of the dynamical system, solely from the measurements. Second, we use concepts and tools from control theory and build a linear contracting observer to estimate the latent variables in a sequential manner from new incoming measurements. The effectiveness of the presented framework is demonstrated by applying it to a toy problem and to a music analysis application. In these examples we show that our method reveals the intrinsic variables of the analyzed dynamical systems.
Boots, Byron
2011-01-01
Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that sol...
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-07-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
An Incremental Manifold Learning Algorithm Based on Iterative Decomposition%一种基于迭代分解的增量流形学习算法
Institute of Scientific and Technical Information of China (English)
谈超; 吉根林
2016-01-01
流形学习可以用于发现大型高维数据集的内在结构,并给出理解该数据集的潜在方式,已被视为一种有效的非线性降维方法.近年来,新数据点不断地从数据流中产生,将改变已有数据点及其邻域点的坐标,传统流形学习算法不能有效地用于寻找高维数据流的内在信息.为了解决该问题,本文提出了一种基于迭代分解的增量流形学习算法IMLID(Incremental Manifold Learning Algorithm Based on Iterative Decomposition),可以检测到数据流形中的逐步变化,校准逐渐变化中的流形,可提高在取样于真实世界的特征集上分类效果的精确率,利用真实数据集进行实验验证,结果表明本文提出的算法是有效的,与其他相关算法相比,其性能具有优势,在模式识别、生物信息等领域具有应用价值.%Manifold learning is used to discover intrinsic low-dimensional manifolds of data points embedded in high-dimensional spaces,which is useful in nonlinear dimension reduction. In recent years,new data points come continually, which will change the existing data points' neighborhoods and their local distributions. Tranditional methods cannot discover intrinsic information of high dimensional data streams effectively. To solve this problem,we propose an Incre?mental Manifold Learning Algorithm Based on Iterative Decomposition(IMLID),which can detect the change of mani?fold and improve the classification accuracy of the feature set sampling in the real world. Experiments on real-life datasets validate the effectiveness of the proposed method which has important significance and extensive application value in pattern recognition and so on.
Incremental and evolutionary manifold learning: a survey%增量与演化流形学习综述
Institute of Scientific and Technical Information of China (English)
谈超; 关佶红; 周水庚
2012-01-01
Manifold learning is to find the low-dimensional smooth manifold of observation data embedded in high-dimensional data space. In recent years, exploring the intrinsic low-dimensional manifold structure online or incrementally becomes a hot research topic in manifold learning area. This paper surveys the state of the art of incremental and evolutionary manifold learning, including the mechanisms and features of major existing incremental and evolutionary manifold learning methods, their advantages and disadvantages, and highlights the open research issues and future research directions.%流形学习的目标是发现观测数据嵌入在高维数据空间中的低维光滑流形.近年来,在线或增量地发现内在低维流形结构成为流形学习的研究热点.从增量学习和演化学习2个方面入手,对该领域已有研究进展进行综述.增量流形学习较之传统的批量流形学习方法具有动态增量的能力,而演化流形学习能够在线地发现海量动态数据的内在规律,有利于进行维数约简和数据分析.文中对主要的增量与演化流形学习算法的基本原理、特点进行了阐述,分析了各自的优点与不足,指出了该领域的开放问题,并对进一步的研究方向进行了展望.
Gene classification using parameter-free semi-supervised manifold learning.
Huang, Hong; Feng, Hailiang
2012-01-01
A new manifold learning method, called parameter-free semi-supervised local Fisher discriminant analysis (pSELF), is proposed to map the gene expression data into a low-dimensional space for tumor classification. Motivated by the fact that semi-supervised and parameter-free are two desirable and promising characteristics for dimension reduction, a new difference-based optimization objective function with unlabeled samples has been designed. The proposed method preserves the global structure of unlabeled samples in addition to separating labeled samples in different classes from each other. The semi-supervised method has an analytic form of the globally optimal solution, which can be computed efficiently by eigen decomposition. Experimental results on synthetic data and SRBCT, DLBCL, and Brain Tumor gene expression data sets demonstrate the effectiveness of the proposed method.
A new strategy for protein interface identification using manifold learning method.
Wang, Bing; Huang, De-Shuang; Jiang, Changjun
2014-06-01
Protein interactions play vital roles in biological processes. The study for protein interface will allow people to elucidate the mechanism of protein interaction. However, a large portion of protein interface data is incorrectly collected in current studies. In this paper, a novel strategy of dataset reconstruction using manifold learning method has been proposed for dealing with the noises in the interaction interface data whose definition is based on the residue distances among the different chains within protein complexes. Three support vector machine-based predictors are constructed using different protein features to identify the functional sites involved in the formation of protein interface. The experimental results achieved in this work demonstrate that our strategy can remove noises, and therefore improve the ability for identification of protein interfaces with 77.8% accuracy.
Directory of Open Access Journals (Sweden)
HongZhong Tang
2016-01-01
Full Text Available Optimizing the mutual coherence of a learned dictionary plays an important role in sparse representation and compressed sensing. In this paper, a efficient framework is developed to learn an incoherent dictionary for sparse representation. In particular, the coherence of a previous dictionary (or Gram matrix is reduced sequentially by finding a new dictionary (or Gram matrix, which is closest to the reference unit norm tight frame of the previous dictionary (or Gram matrix. The optimization problem can be solved by restricting the tightness and coherence alternately at each iteration of the algorithm. The significant and different aspect of our proposed framework is that the learned dictionary can approximate an equiangular tight frame. Furthermore, manifold optimization is used to avoid the degeneracy of sparse representation while only reducing the coherence of the learned dictionary. This can be performed after the dictionary update process rather than during the dictionary update process. Experiments on synthetic and real audio data show that our proposed methods give notable improvements in lower coherence, have faster running times, and are extremely robust compared to several existing methods.
TU-F-BRF-06: 3D Pancreas MRI Segmentation Using Dictionary Learning and Manifold Clustering
Energy Technology Data Exchange (ETDEWEB)
Gou, S; Rapacchi, S; Hu, P; Sheng, K [UCLA School of Medicine, Los Angeles, CA (United States)
2014-06-15
Purpose: The recent advent of MRI guided radiotherapy machines has lent an exciting platform for soft tissue target localization during treatment. However, tools to efficiently utilize MRI images for such purpose have not been developed. Specifically, to efficiently quantify the organ motion, we develop an automated segmentation method using dictionary learning and manifold clustering (DLMC). Methods: Fast 3D HASTE and VIBE MR images of 2 healthy volunteers and 3 patients were acquired. A bounding box was defined to include pancreas and surrounding normal organs including the liver, duodenum and stomach. The first slice of the MRI was used for dictionary learning based on mean-shift clustering and K-SVD sparse representation. Subsequent images were iteratively reconstructed until the error is less than a preset threshold. The preliminarily segmentation was subject to the constraints of manifold clustering. The segmentation results were compared with the mean shift merging (MSM), level set (LS) and manual segmentation methods. Results: DLMC resulted in consistently higher accuracy and robustness than comparing methods. Using manual contours as the ground truth, the mean Dices indices for all subjects are 0.54, 0.56 and 0.67 for MSM, LS and DLMC, respectively based on the HASTE image. The mean Dices indices are 0.70, 0.77 and 0.79 for the three methods based on VIBE images. DLMC is clearly more robust on the patients with the diseased pancreas while LS and MSM tend to over-segment the pancreas. DLMC also achieved higher sensitivity (0.80) and specificity (0.99) combining both imaging techniques. LS achieved equivalent sensitivity on VIBE images but was more computationally inefficient. Conclusion: We showed that pancreas and surrounding normal organs can be reliably segmented based on fast MRI using DLMC. This method will facilitate both planning volume definition and imaging guidance during treatment.
Jiang, Lu-Lu; Luo, Mei-Fu; Zhang, Yu; Yu, Xin-Jie; Kong, Wen-Wen; Liu, Fei
2014-01-01
An identification method based on sparse representation (SR) combined with autoencoder network (AN) manifold learning was proposed for discriminating the varieties of transmission fluid by using near infrared (NIR) spectroscopy technology. NIR transmittance spectra from 600 to 1 800 nm were collected from 300 transmission fluid samples of five varieties (each variety consists of 60 samples). For each variety, 30 samples were randomly selected as training set (totally 150 samples), and the rest 30 ones as testing set (totally 150 samples). Autoencoder network manifold learning was applied to obtain the characteristic information in the 600-1800 nm spectra and the number of characteristics was reduced to 10. Principal component analysis (PCA) was applied to extract several relevant variables to represent the useful information of spectral variables. All of the training samples made up a data dictionary of the sparse representation (SR). Then the transmission fluid variety identification problem was reduced to the problem as how to represent the testing samples from the data dictionary (training samples data). The identification result thus could be achieved by solving the L-1 norm-based optimization problem. We compared the effectiveness of the proposed method with that of linear discriminant analysis (LDA), least squares support vector machine (LS-SVM) and sparse representation (SR) using the relevant variables selected by principal component analysis (PCA) and AN. Experimental results demonstrated that the overall identification accuracy of the proposed method for the five transmission fluid varieties was 97.33% by AN-SR, which was significantly higher than that of LDA or LS-SVM. Therefore, the proposed method can provide a new effective method for identification of transmission fluid variety.
Discrete time learning control in nonlinear systems
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Web Document Classification Algorithm Based on Manifold Learning and SVM%基于流形学习和SVM的Web文档分类算法
Institute of Scientific and Technical Information of China (English)
王自强; 钱旭
2009-01-01
为解决Web文档分类问题,提出一种基于流形学习和SVM的Web文档分类算法.该算法利用流形学习算法LPP对训练集中的高维Web文档空间进行非线性降维,从中找出隐藏在高维观测数据中有意义的低维结构,在降维后的低维特征空间中利用乘性更新规则的优化SVM进行分类预测.实验结果表明该算法以较少的运行时间获得更高的分类准确率.%To efficiently resolve Web document classification problem, a novel Web document classification algorithm based on manifold learning and Support Vector Machine(SVM) is proposed. The high dimensional Web document space in the training sets are non-linearly reduced to lower dimensional space with manifold learning algorithm LPP, and the hidden interesting lower dimensional structure can be discovered from the high dimensional observisional data. The classification and predication in the lower dimensional feature space are implemented with the multiplicative update-based optimal SVM. Experimental results show that the algorithm achieves higher classification accuracy with less running time.
Self-organised manifold learning and heuristic charting via adaptive metrics
Horvath, Denis; Ulicny, Jozef; Brutovsky, Branislav
2016-01-01
Classical metric and non-metric multidimensional scaling (MDS) variants represent the well-known manifold learning (ML) methods which enable construction of low-dimensional representation (projections) of high-dimensional data inputs. However, their use is limited to the cases when data are inherently reducible to low dimensionality. In general, drawbacks and limitations of these, as well as pure, MDS variants become more apparent when the exploration (learning) is exposed to the structured data of high intrinsic dimension. As we demonstrate on artificial as well as real-world datasets, the over-determination problem can be solved by means of the hybrid and multi-component discrete-continuous multi-modal optimisation heuristics. A remarkable feature of the approach is that projections onto 2D are constructed simultaneously with the data categorisation compensating in part for the loss of original input information. We observed that the optimisation module integrated with ML modelling, metric learning and categorisation leads to a nontrivial mechanism resulting in heuristic charting of data.
Cruz-Barbosa, Raúl; Vellido, Alfredo
2011-02-01
Medical diagnosis can often be understood as a classification problem. In oncology, this typically involves differentiating between tumour types and grades, or some type of discrete outcome prediction. From the viewpoint of computer-based medical decision support, this classification requires the availability of accurate diagnoses of past cases as training target examples. The availability of such labeled databases is scarce in most areas of oncology, and especially so in neuro-oncology. In such context, semi-supervised learning oriented towards classification can be a sensible data modeling choice. In this study, semi-supervised variants of Generative Topographic Mapping, a model of the manifold learning family, are applied to two neuro-oncology problems: the diagnostic discrimination between different brain tumour pathologies, and the prediction of outcomes for a specific type of aggressive brain tumours. Their performance compared favorably with those of the alternative Laplacian Eigenmaps and Semi-Supervised SVM for Manifold Learning models in most of the experiments.
Image-based human age estimation by manifold learning and locally adjusted robust regression.
Guo, Guodong; Fu, Yun; Dyer, Charles R; Huang, Thomas S
2008-07-01
Estimating human age automatically via facial image analysis has lots of potential real-world applications, such as human computer interaction and multimedia communication. However, it is still a challenging problem for the existing computer vision systems to automatically and effectively estimate human ages. The aging process is determined by not only the person's gene, but also many external factors, such as health, living style, living location, and weather conditions. Males and females may also age differently. The current age estimation performance is still not good enough for practical use and more effort has to be put into this research direction. In this paper, we introduce the age manifold learning scheme for extracting face aging features and design a locally adjusted robust regressor for learning and prediction of human ages. The novel approach improves the age estimation accuracy significantly over all previous methods. The merit of the proposed approaches for image-based age estimation is shown by extensive experiments on a large internal age database and the public available FG-NET database.
Shiota, Masahiro
1987-01-01
A Nash manifold denotes a real manifold furnished with algebraic structure, following a theorem of Nash that a compact differentiable manifold can be imbedded in a Euclidean space so that the image is precisely such a manifold. This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds. Basic to the theory is an algebraic analogue of Whitney's Approximation Theorem. This theorem induces a "finiteness" of Nash manifold structures and differences between Nash and differentiable manifolds. The point of view of the author is topological. However the proofs also require results and techniques from other domains so elementary knowledge of commutative algebra, several complex variables, differential topology, PL topology and real singularities is required of the reader. The book is addressed to graduate students and researchers in differential topology and real algebra...
Erem, Burak; Martinez Orellana, Ramon; Hyde, Damon E.; Peters, Jurriaan M.; Duffy, Frank H.; Stovicek, Petr; Warfield, Simon K.; MacLeod, Rob S.; Tadmor, Gilead; Brooks, Dana H.
2016-04-01
This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.
Ensemble manifold regularization.
Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng
2012-06-01
We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.
基于核融合的多信息流形学习算法%Multi-information manifold learning algorithm based on kernel fusion
Institute of Scientific and Technical Information of China (English)
刘元; 吴小俊
2016-01-01
流形学习算法可分为全局流形学习与局部流形学习，它们分别保持了流形上的全局特征信息与局部特征信息，但是实验证明仅基于全局特征或局部特征信息的流形学习算法不能很好地保持真实的流形结构，影响了学习效果。基于流形学习的核的视角，融合了全局流形学习算法 ISOMAP 与局部流形学习算法 LTSA 的核矩阵，提出了可以同时保持流形结构的全局特征信息与局部特征信息的流形学习算法。在人工数据集和人脸图像集上的仿真实验验证了该算法的有效性。%Manifold learning algorithms can be divided into global manifold learning and local manifold learning,and they keep global features and local features of manifolds respectively.However,experiments show that manifold learning algorithm based only on global or local feature information can not maintain the real structure of manifold well which affects the results of manifold learning.Therefore,in the view of kernel,this paper proposed a multi-information manifold learning algorithm based on the kernel fusion of the ISOMAP and LTSA.The proposed algorithm can maintain the global and local features of manifolds synchronously,and the experimental results on several synthetic data and standard face databases indicate the effectiveness of the algorithm.
Manifold learning for dimensionality reduction and clustering of skin spectroscopy data
Safi, Asad; Castañeda, Victor; Lasser, Tobias; Mateus, Diana C.; Navab, Nassir
2011-03-01
Diagnosis of benign and malign skin lesions is currently done mostly relying on visual assessment and frequent biopsies performed by dermatologists. As the timely and correct diagnosis of these skin lesions is one of the most important factors in the therapeutic outcome, leveraging new technologies to assist the dermatologist seems natural. Optical spectroscopy is a technology that is being established to aid skin lesion diagnosis, as the multi-spectral nature of this imaging method allows to detect multiple physiological changes like those associated with increased vasculature, cellular structure, oxygen consumption or edema in tumors. However, spectroscopy data is typically very high dimensional (on the order of thousands), which causes difficulties in visualization and classification. In this work we apply different manifold learning techniques to reduce the dimensions of the input data and get clustering results. Spectroscopic data of 48 patients with suspicious and actually malignant lesions was analyzed using ISOMAP, Laplacian Eigenmaps and Diffusion Maps with varying parameters and compared to results using PCA. Using optimal parameters, both ISOMAP and Laplacian Eigenmaps could cluster the data into suspicious and malignant with 96% accuracy, compared to the diagnosis of the treating physicians.
Manifold learning for the emulation of spatial fields from computational models
Xing, W. W.; Triantafyllidis, V.; Shah, A. A.; Nair, P. B.; Zabaras, N.
2016-12-01
Repeated evaluations of expensive computer models in applications such as design optimization and uncertainty quantification can be computationally infeasible. For partial differential equation (PDE) models, the outputs of interest are often spatial fields leading to high-dimensional output spaces. Although emulators can be used to find faithful and computationally inexpensive approximations of computer models, there are few methods for handling high-dimensional output spaces. For Gaussian process (GP) emulation, approximations of the correlation structure and/or dimensionality reduction are necessary. Linear dimensionality reduction will fail when the output space is not well approximated by a linear subspace of the ambient space in which it lies. Manifold learning can overcome the limitations of linear methods if an accurate inverse map is available. In this paper, we use kernel PCA and diffusion maps to construct GP emulators for very high-dimensional output spaces arising from PDE model simulations. For diffusion maps we develop a new inverse map approximation. Several examples are presented to demonstrate the accuracy of our approach.
EEG-based emotion recognition with manifold regularized extreme learning machine.
Peng, Yong; Zhu, Jia-Yi; Zheng, Wei-Long; Lu, Bao-Liang
2014-01-01
EEG signals, which can record the electrical activity along the scalp, provide researchers a reliable channel for investigating human emotional states. In this paper, a new algorithm, manifold regularized extreme learning machine (MRELM), is proposed for recognizing human emotional states (positive, neutral and negative) from EEG data, which were previously evoked by watching different types of movie clips. The MRELM can simultaneously consider the geometrical structure and discriminative information in EEG data. Using differential entropy features across whole five frequency bands, the average accuracy of MRELM is 81.01%, which is better than those obtained by GELM (80.25%) and SVM (76.62%). The accuracies obtained from high frequency band features (β, γ) are obviously superior to those of low frequency band features, which shows β and γ bands are more relevant to emotional states transition. Moreover, experiments are conducted to further evaluate the efficacy of MRELM, where the training and test sets are from different sessions. The results demonstrate that the proposed MRELM is a competitive model for EEG-based emotion recognition.
Discriminative Manifold Learning Based Detection of Movement-Related Cortical Potentials.
Lin, Chuang; Wang, Bing-Hui; Jiang, Ning; Xu, Ren; Mrachacz-Kersting, Natalie; Farina, Dario
2016-09-01
The detection of voluntary motor intention from EEG has been applied to closed-loop brain-computer interfacing (BCI). The movement-related cortical potential (MRCP) is a low frequency component of the EEG signal, which represents movement intention, preparation, and execution. In this study, we aim at detecting MRCPs from single-trial EEG traces. For this purpose, we propose a detector based on a discriminant manifold learning method, called locality sensitive discriminant analysis (LSDA), and we test it in both online and offline experiments with executed and imagined movements. The online and offline experimental results demonstrated that the proposed LSDA approach for MRCP detection outperformed the Locality Preserving Projection (LPP) approach, which was previously shown to be the most accurate algorithm so far tested for MRCP detection. For example, in the online tests, the performance of LSDA was superior than LPP in terms of a significant reduction in false positives (FP) (passive FP: 1.6 ±0.9/min versus 2.9 ±1.0/min, p = 0.002, active FP: 2.2 ±0.8/min versus 2.7 ±0.6/min , p = 0.03 ), for a similar rate of true positives. In conclusion, the proposed LSDA based MRCP detection method is superior to previous approaches and is promising for developing patient-driven BCI systems for motor function rehabilitation as well as for neuroscience research.
Institute of Scientific and Technical Information of China (English)
孙伟伟; 刘春; 施蓓琦; 李巍岳
2012-01-01
将Isomap流形学习方法应用于高光谱影像非线性降维时,在构建最短路径过程中,其边界点往往被忽略而没有低维流形坐标。对此,引入偏最小二乘方法来模拟修复遗失点的流形坐标,并从两个方面进行了综合评价。实验结果表明,模拟流形坐标与实际坐标吻合很好。%As a manifold learning method,Isomap has been widely used for making nonlinearly reduction for hyperspectral image.However,during the construction process of the shortest path graph,the boundary points,which are not noise points,have always been omitted for the consideration of the stability of the graph.Therefore,the PLS method is introduced to repair and simulate the manifold coordinates of the lost points in the shortest path graph.And the simulated manifold coordinates have been evaluated from two different aspects to verify our method.The results show that the simulated manifold coordinates agree well with the real one.It will be quite useful for further classification or visualization with low dimensional manifold image.
基于边界检测的多流形学习算法%Multi-manifold Learning Based on Boundary Detection
Institute of Scientific and Technical Information of China (English)
邹鹏; 李凡长; 尹宏伟; 张莉; 张召
2016-01-01
已知流形学习算法都假设数据分布于一个单流形,而现实中大部分数据都分布在多流形上,因此限制算法的实际应用.基于此种情况,文中提出基于边界检测的多流形学习算法,通过检测流形的边界处理分布于多流形的数据,并且可以较好地保持流形内、流形间的测地距离.算法首先检测流形边界,再分别降维处理各流形,最后将各低维坐标重置于一个全局坐标系中.在人工数据集和真实数据集上的对比实验表明文中算法的可行性和有效性.%In manifold learning algorithms, the data are assumed to be aligned on a single manifold. The application of algorithms is limited due to the general distribution of practical datasets on multiple manifolds. In this paper, multi-manifold learning based on boundary detection( MBD) is proposed. By the proposed method, data of distribution on several manifolds are efficiently learned through boundary detection and intra and inter manifolds geodesic distances can be kept faithfully. Firstly the boundary of data manifolds is detected and then the dimensionality of the manifolds is reduced separately. Finally, low dimensional coordinates are relocated into a global coordinate system. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated through experiments on both synthetic and real datasets.
A Classification Method Based on Manifold Learning for Gene Microarray Data%基于流形学习的基因微阵列数据分类方法
Institute of Scientific and Technical Information of China (English)
李强; 石陆魁; 刘恩海; 王歌
2012-01-01
Each sample in gene microarray data contains thousands or even tens of thousands of genes. It is necessary to reduce the dimension of the data before classifying them for obtaining better classified results. Manifold learning, as a nonlinear dimension reduction method, can discover the intrinsic laws hidden in the high dimensional data and has been widely applied in areas such as pattern recognition. A model combining manifold learning with classified algorithms was proposed to classify microarray data. In the model, the dimension of microarray data was firstly reduced with some manifold learning method. Then the data reduced the dimension were classified. In experiments, several manifold learning algorithms including LLE, ISOMAP, LE and LTSA are combined with three classified methods. And the results are compared with those from directly classifying high dimensional data. Experiments showed that the classification accuracy was great improved with the proposed model. Moreover, the execute efficiency of classification algorithms was also greatly increased.%提出了一种结合流形学习方法与分类算法的基因微阵列数据分类模型,先用流形学习算法对基因微阵列数据进行降维处理,然后再对降维后的数据进行分类.在实验中将流形学习算法LLE、ISOMAP、LE和LTSA与三种分类算法相结合,并与直接用高维数据进行分类的结果进行了比较,实验结果表明所提出的模型极大地提高了分类精度,同时也提高了分类算法的执行效率.
Lu, Shen; Xia, Yong; Cai, Tom Weidong; Feng, David Dagan
2015-01-01
Dementia, Alzheimer's disease (AD) in particular is a global problem and big threat to the aging population. An image based computer-aided dementia diagnosis method is needed to providing doctors help during medical image examination. Many machine learning based dementia classification methods using medical imaging have been proposed and most of them achieve accurate results. However, most of these methods make use of supervised learning requiring fully labeled image dataset, which usually is not practical in real clinical environment. Using large amount of unlabeled images can improve the dementia classification performance. In this study we propose a new semi-supervised dementia classification method based on random manifold learning with affinity regularization. Three groups of spatial features are extracted from positron emission tomography (PET) images to construct an unsupervised random forest which is then used to regularize the manifold learning objective function. The proposed method, stat-of-the-art Laplacian support vector machine (LapSVM) and supervised SVM are applied to classify AD and normal controls (NC). The experiment results show that learning with unlabeled images indeed improves the classification performance. And our method outperforms LapSVM on the same dataset.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We determine the asymptotic order of entropy number and optimal non - linear approximations of anisotropic periodic Besov class of Brpθ(Td) (1≤p≤∞, 1≤θ≤∞ ) by manifolds of finite pseudo-dimension in the metric Lq (Td), 1≤ q≤∞, where Td is the d-dimensional torus.
高职计算机网络专业课程体系建设%Analysis of Some Problems in Manifold Learning of LLE
Institute of Scientific and Technical Information of China (English)
韩起云
2012-01-01
Aiming at the problem of nonlinear dimensionality reduction, presents local linear embedding （LLE）algorithm. The nonlinear structure in high dimensional data space is exploited with the local symmetries of linear reconstructions. Maps the data points in high dimensional space into corresponding data points in lower dimensional space under preserving distance between data points. Introduces a manifold learning algorithm of LLE, summarizes some problems of LLE and its research status, and discusses the prospect of LLE.%分析目前网络专业毕业生的就业现状以及导致此现状的原因．给出市场上需要的网络人才类型以及具体的网络就业岗位群。根据网络专业就业岗位群设计出网络专业的课程体系．并对课程体系进行详细的分析。结合我院实际情况给出网络课程体系实施过程中的几点建议。
Algorithm of Supervised Learning on Outlier Manifold%有监督的噪音流形学习算法
Institute of Scientific and Technical Information of China (English)
黄添强; 李凯; 郑之
2011-01-01
流形学习算法是维度约简与数据可视化领域的重要工具,提高算法的效率与健壮性对其实际应用有积极意义.经典的流形学习算法普遍的对噪音点较为敏感,现有的改进算法尚存在不足.本文提出一种基于监督学习与核函数的健壮流形学习算法,把核方法与监督学习引入降维过程,利用已知标签数据信息与核函数特性,使得同类样本变得紧密,不同类样本变成分散,提高后续分类任务的效果,降低算法对流形上噪音的敏感性.在UCI数据与白血病拉曼光谱数据上的实验表明本文改进的算法具有更高的抗噪性.%Manifold learning algorithm is an important tool in the field of dimension reduction and data visualization. Improving the algorithm's efficiency and robustness is of positive significance to its practical application. Classical manifold learning algorithm is sensitive to noise points,and its improved algorithms have been imperfect. This paper presents a robust manifold learning algorithm based on supervised learning and kernel function. It introduces nuclear methods and supervised learning into the dimensionality reduction ,and takes full advantage of the label of some data and the property of kernel function. The proposed algorithm can make close and same types of samples and distribute different types of samples,thus to improves the effect of the classification task and reduce the noise sensitivity of outliers on manifold. The experiments on the UCI data and Raman data of leukemia reveal that the algorithm has better noise immunity.
Diffusion Harmonics and Dual Geometry on Carnot Manifolds
Constantin, Sarah
The "curse of dimensionality" motivates the importance of techniques for computing low-dimensional approximations of high-dimensional data. It is often necessary to use nonlinear techniques to recover a low-dimensional manifold embedded via a nonlinear map in a high-dimensional space; this family of techniques is referred to as "manifold learning." The accuracy of manifold-learning-based approximations is founded on asymptotic results that assume the data is drawn from a low-dimensional Riemannian manifold. However, in natural datasets, this assumption is often overly restrictive. In the first part of this thesis we examine a more general class of manifolds known as Carnot manifolds, a type of sub-Riemannian manifold that governs natural phenomena such as chemical kinetics and configuration spaces of jointed objects. We find that diffusion maps can be generalized to Carnot manifolds and that the projection onto diffusion harmonics gives an almost isometric embedding; as a side effect, the diffusion distance is a computationally fast estimate for the shortest distance between two points on a Carnot manifold. We apply this theory to biochemical network data and observe that the chemical kinetics of the EGFR network are governed by a Carnot, but not Riemannian, manifold. In the second part of this thesis we examine the Heisenberg group, a classical example of a Carnot manifold. We obtain a representation-theoretic proof that the eigenfunctions of the sub-Laplacian on SU(2) approach the eigenfunctions of the sub-Laplacian on the Heisenberg group, in the limit as the radius of the sphere becomes large, in analogy with the limiting relationship between the Fourier series on the circle and the Fourier transform on the line. This result also illustrates how projecting onto the sub-Laplacian eigenfunctions of a non-compact Carnot manifold can be locally approximated by projecting onto the sub-Laplacian eigenfunctions of a tangent compact Carnot manifold. In the third part
On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.
Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba
2013-01-01
Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ (d) , and the dictionary is learned from the training data using the vector space structure of ℝ (d) and its Euclidean L(2)-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.
Manifold learning based ECG-free free-breathing cardiac CINE MRI.
Usman, Muhammad; Atkinson, David; Kolbitsch, Christoph; Schaeffter, Tobias; Prieto, Claudia
2015-06-01
To present and validate a manifold learning (ML)-based method that can estimate both cardiac and respiratory navigator signals from electrocardiogram (ECG)-free free-breathing cardiac magnetic resonance imaging (MRI) data to achieve self-gated retrospective CINE reconstruction. In this work the use of the ML method is demonstrated for 2D cardiac CINE to achieve both cardiac and respiratory self-gating without the need of an external navigator or ECG signal. This is achieved by sequentially applying ML to two sets of retrospectively reconstructed real-time images with differing temporal resolutions. A 1D cardiac signal is estimated by applying ML to high temporal resolution real-time images reconstructed from the acquired data. Using the estimated cardiac signal, a 1D respiratory signal was obtained by applying the ML method to low temporal resolution images reconstructed from the same acquired data for each cardiac cycle. Data were acquired in five volunteers with a 2D golden angle radial trajectory in a balanced steady-state free precession (b-SSFP) acquisition. The accuracy of the estimated cardiac signal was calculated as the standard deviation of the temporal difference between the estimated signal and the recorded ECG. The correlation between the estimated respiratory signal and standard pencil beam navigator signal was evaluated. Gated CINE reconstructions (20 cardiac phases per cycle, temporal resolution ∼30 msec) using the estimated cardiac and respiratory signals were qualitatively compared against conventional ECG-gated breath-hold CINE acquisitions. Accurate cardiac signals were estimated with the proposed method, with an error standard deviation in comparison to ECG lower than 20 msec. Respiratory signals estimated with the proposed method achieved a mean cross-correlation of 94% with respect to standard pencil beam navigator signals. Good quality visual scores of 2.80 ± 0.45 (scores from 0, bad, to 4, excellent quality) were observed for the
Distributed Extreme Learning Machine for Nonlinear Learning over Network
Directory of Open Access Journals (Sweden)
Songyan Huang
2015-02-01
Full Text Available Distributed data collection and analysis over a network are ubiquitous, especially over a wireless sensor network (WSN. To our knowledge, the data model used in most of the distributed algorithms is linear. However, in real applications, the linearity of systems is not always guaranteed. In nonlinear cases, the single hidden layer feedforward neural network (SLFN with radial basis function (RBF hidden neurons has the ability to approximate any continuous functions and, thus, may be used as the nonlinear learning system. However, confined by the communication cost, using the distributed version of the conventional algorithms to train the neural network directly is usually prohibited. Fortunately, based on the theorems provided in the extreme learning machine (ELM literature, we only need to compute the output weights of the SLFN. Computing the output weights itself is a linear learning problem, although the input-output mapping of the overall SLFN is still nonlinear. Using the distributed algorithmto cooperatively compute the output weights of the SLFN, we obtain a distributed extreme learning machine (dELM for nonlinear learning in this paper. This dELM is applied to the regression problem and classification problem to demonstrate its effectiveness and advantages.
Regularized manifold information extreme learning machine%正则化流形信息极端学习机
Institute of Scientific and Technical Information of China (English)
刘德山; 楚永贺; 闫德勤
2016-01-01
By exploiting the thought of manifold learning and its theoretical method, a regularized manifold information ex-treme learning machine algorithm aimed to depict and fully utilize manifold information was proposed. The proposed algo-rithm exploited the geometry and discrimination manifold information of data to perform network of ELM. The proposed algorithm could overcome the problem of the overlap of information. Singular problems of inter-class and within-class were solved effectively by using maximum margin criterion. The problem of inadequate learning with limited samples was solved. In order to demonstrate the effectiveness, comparative experiments with ELM and the related update algorithms RAFELM, GELM were conducted using the commonly used image data. Experimental results show that the proposed algorithm can significantly improve the generalization performance of ELM and outperforms the related update algorithms.%基于流形学习的思想和理论方法，提出刻画流形信息的正则化的极端学习机(MELM)算法。该算法利用流形信息刻画数据的几何结构和判别信息，克服 ELM 在有限样本上学习不充分的问题；能够有效提取数据样本的判别信息避免数据样本信息重叠；利用最大边际准则有效解决类间散度矩阵和类内散度矩阵的奇异问题。为验证所提方法的有效性，实验使用普遍应用的图像数据，将 MELM 与 ELM 以及相关最新算法 RAFELM、GELM进行识别率和计算效率的对比。实验结果表明，该算法能够显著提高 ELM 的分类准确率和泛化能力，并且优于其他相关算法。
Sparks, Rachel; Madabhushi, Anant
2012-03-01
Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides, subtle morphologic and architectural differences of histological attributes may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a manifold constrained by the SSMM. We
Institute of Scientific and Technical Information of China (English)
ZHOU Ming-gang; HUANG Qi-bai; WANG Yong; XU Zhi-sheng
2007-01-01
This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.
一种选择标注分层流形学习算法%A Selecting Landmark Hierarchical Manifold Learning Algorithm
Institute of Scientific and Technical Information of China (English)
范自立; 李凡长
2011-01-01
The manifold data query needs the manifold embedded representation. Thus it often involves accessing considerable volume of data. An approach of hierarchical manifold learning algorithm based on selecting landmark points from the given samples is proposed for representing data on manifold. The landmarks set can help locate the novel points on the data manifold. Firstly, an adaptive nearest neighbor' s method is employed to extract the nearest neighborhood of each data. Then the geodesic matrix is constructed. Finally, a landmark point is randomly selected in landmark point set, and its maximum cell is found till the manifold set is empty and the rough landmark point set is formed. In addition, the landpoint set is optimized. The experimental results prove that the proposed method preserves the topological features of manifold, and it helps inquire the manifold data efficiently.%流形数据的查询需要使用流形的嵌入表示,因此查询流形数据需要访问大量的样本数据.提出一种选择标注分层流形学习算法,选择出的标注点集用来帮助查找流形数据.首先采用自适应近邻算法求出每个数据的最优近邻,然后构造测地线矩阵,最后逐步迭代随机选择标注点,求出每个标注点的极大单元子集,直到流形数据集变成空集,形成初始标注点集.此外,还要优化标注点集.实验结果证明所选择的标注点集保持流形的拓扑特性,可有效帮助查询流形数据.
Directory of Open Access Journals (Sweden)
Pąk Karol
2015-02-01
Full Text Available Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary, i.e. where each point has a neighborhood that is homeomorphic to a closed ball of En for some n.
Kosinski, Antoni A
2007-01-01
The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho
Manifold Matching for High-Dimensional Pattern Recognition
HOTTA, Seiji
2008-01-01
In this chapter manifold matching for high-dimensional pattern classification was described. The topics described in this chapter were summarized as follows: The meaning and effectiveness of manifold matching The similarity between various classifiers from the point of view of manifold matching Accuracy improvement for manifold matching Learning rules for manifold matching Experimental results on handwritten digit datasets showed that manifold matching achieved lower error rates than other cl...
Topping, T. Russell; French, James; Hancock, Monte F., Jr.
2010-04-01
Working with the Naval Research Laboratory, Celestech has implemented advanced non-linear hyperspectral image (HSI) processing algorithms optimized for Graphics Processing Units (GPU). These algorithms have demonstrated performance improvements of nearly 2 orders of magnitude over optimal CPU-based implementations. The paper briefly covers the architecture of the NIVIDIA GPU to provide a basis for discussing GPU optimization challenges and strategies. The paper then covers optimization approaches employed to extract performance from the GPU implementation of Dr. Bachmann's algorithms including memory utilization and process thread optimization considerations. The paper goes on to discuss strategies for deploying GPU-enabled servers into enterprise service oriented architectures. Also discussed are Celestech's on-going work in the area of middleware frameworks to provide an optimized multi-GPU utilization and scheduling approach that supports both multiple GPUs in a single computer as well as across multiple computers. This paper is a complementary work to the paper submitted by Dr. Charles Bachmann entitled "A Scalable Approach to Modeling Nonlinear Structure in Hyperspectral Imagery and Other High-Dimensional Data Using Manifold Coordinate Representations". Dr. Bachmann's paper covers the algorithmic and theoretical basis for the HSI processing approach.
Learning Inverse Rig Mappings by Nonlinear Regression.
Holden, Daniel; Saito, Jun; Komura, Taku
2016-11-11
We present a framework to design inverse rig-functions - functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.
You, Tao; Cheng, Hui-Min; Ning, Yi-Zi; Shia, Ben-Chang; Zhang, Zhong-Yuan
2016-12-01
Like clustering analysis, community detection aims at assigning nodes in a network into different communities. Fdp is a recently proposed density-based clustering algorithm which does not need the number of clusters as prior input and the result is insensitive to its parameter. However, Fdp cannot be directly applied to community detection due to its inability to recognize the community centers in the network. To solve the problem, a new community detection method (named IsoFdp) is proposed in this paper. First, we use IsoMap technique to map the network data into a low dimensional manifold which can reveal diverse pair-wised similarity. Then Fdp is applied to detect the communities in the network. An improved partition density function is proposed to select the proper number of communities automatically. We test our method on both synthetic and real-world networks, and the results demonstrate the effectiveness of our algorithm over the state-of-the-art methods.
Supervised Multi-Manifold Learning Algorithm Based on ISOMAP%基于等距映射的监督多流形学习算法
Institute of Scientific and Technical Information of China (English)
邵超; 万春红
2014-01-01
The existing supervised multi-manifold learning algorithms adjust the distances between data points according to their class labels, and hence the multiple manifolds can be classified successfully. However, the poor generalization ability of these algorithms results in unfaithful display of the intrinsic geometric structure of some manifolds. A supervised multi-manifold learning algorithm based on Isometric mapping ( ISOMAP) is proposed. The shortest path algorithm suitable for the multi-manifold structure is used to compute the shortest path distances which can effectively approximate the corresponding geodesic distances even in the multi-manifold structure. Then, Sammon mapping is used to further preserve shorter distances in the low-dimensional embedding space. Consequently, the intrinsic geometric structure of each manifold can be faithfully displayed. Moreover, the manifolds of new data points can be precisely judged based on the similarities between neighboring local tangent spaces according to the local Euclidean nature of the manifold, and thus the proposed algorithm obtains a good generalization ability. The effectiveness of the proposed algorithm is verified by experimental results.%目前的监督多流形学习算法大多数都根据数据的类别标记对彼此间的距离进行调整，能较好实现多流形的分类，但难以成功展现各流形的内在几何结构，泛化能力也较差，因此文中提出一种基于等距映射的监督多流形学习算法。该算法采用适合于多流形的最短路径算法，得到在多流形下依然能正确逼近相应测地距离的最短路径距离，并采用Sammon映射以更好地保持短距离，最终可成功展现各流形的内在几何结构。此外，该算法根据邻近局部切空间的相似性可准确判定新数据点所在的流形，从而具有较强的泛化能力。该算法的有效性可通过实验结果得以证实。
Indian Academy of Sciences (India)
Sarika Goyal; K Sreenadh
2015-11-01
In this article, we study the existence and multiplicity of non-negative solutions of the following p-fractional equation: \\begin{equation*} \\left\\{ \\begin{matrix} -2 {\\displaystyle\\int}_{\\mathbb{R}^n} \\frac{|u(y) - u (x)|^{p-2} (u(y)-u(x))}{|x-y|^{n+p}} dy = h (x) |u|^{q-1} u + b (x)|u|^{r-1} u \\text{ in } ,\\\\ u = 0 \\quad \\text{ in } \\mathbb{R}^n \\setminus , \\quad u \\in W^{,p} (\\mathbb{R}^n) \\end{matrix} \\right. \\end{equation*} where is a bounded domain in $\\mathbb{R}^n$ with continuous boundary, $p ≥ 2$, $n > p $, $ \\in (0,1)$, $0 < q < p -1 < r < p^* - 1$ with $p^* = np (n -p)^{-1}$, $ > 0$ and $h, b$ are signchanging continuous functions. We show the existence and multiplicity of solutions by minimization on the suitable subset of Nehari manifold using the fibering maps. We find that there exists 0 such that for $ \\in (0, _0)$, it has at least two non-negative solutions.
Nonlinear Deep Kernel Learning for Image Annotation.
Jiu, Mingyuan; Sahbi, Hichem
2017-02-08
Multiple kernel learning (MKL) is a widely used technique for kernel design. Its principle consists in learning, for a given support vector classifier, the most suitable convex (or sparse) linear combination of standard elementary kernels. However, these combinations are shallow and often powerless to capture the actual similarity between highly semantic data, especially for challenging classification tasks such as image annotation. In this paper, we redefine multiple kernels using deep multi-layer networks. In this new contribution, a deep multiple kernel is recursively defined as a multi-layered combination of nonlinear activation functions, each one involves a combination of several elementary or intermediate kernels, and results into a positive semi-definite deep kernel. We propose four different frameworks in order to learn the weights of these networks: supervised, unsupervised, kernel-based semisupervised and Laplacian-based semi-supervised. When plugged into support vector machines (SVMs), the resulting deep kernel networks show clear gain, compared to several shallow kernels for the task of image annotation. Extensive experiments and analysis on the challenging ImageCLEF photo annotation benchmark, the COREL5k database and the Banana dataset validate the effectiveness of the proposed method.
Killing Symmetry on Finsler Manifold
Ootsuka, Takayoshi; Ishida, Muneyuki
2016-01-01
Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\\delta K^\\flat =0$ by using the Killing non-linear 1-form $K^\\flat$ and the spray operator $\\delta$ with the Finsler non-linear connection. $K^\\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\\delta K^\\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.
Directory of Open Access Journals (Sweden)
Chao Wei
Full Text Available Topic models and neural networks can discover meaningful low-dimensional latent representations of text corpora; as such, they have become a key technology of document representation. However, such models presume all documents are non-discriminatory, resulting in latent representation dependent upon all other documents and an inability to provide discriminative document representation. To address this problem, we propose a semi-supervised manifold-inspired autoencoder to extract meaningful latent representations of documents, taking the local perspective that the latent representation of nearby documents should be correlative. We first determine the discriminative neighbors set with Euclidean distance in observation spaces. Then, the autoencoder is trained by joint minimization of the Bernoulli cross-entropy error between input and output and the sum of the square error between neighbors of input and output. The results of two widely used corpora show that our method yields at least a 15% improvement in document clustering and a nearly 7% improvement in classification tasks compared to comparative methods. The evidence demonstrates that our method can readily capture more discriminative latent representation of new documents. Moreover, some meaningful combinations of words can be efficiently discovered by activating features that promote the comprehensibility of latent representation.
Wei, Chao; Luo, Senlin; Ma, Xincheng; Ren, Hao; Zhang, Ji; Pan, Limin
2016-01-01
Topic models and neural networks can discover meaningful low-dimensional latent representations of text corpora; as such, they have become a key technology of document representation. However, such models presume all documents are non-discriminatory, resulting in latent representation dependent upon all other documents and an inability to provide discriminative document representation. To address this problem, we propose a semi-supervised manifold-inspired autoencoder to extract meaningful latent representations of documents, taking the local perspective that the latent representation of nearby documents should be correlative. We first determine the discriminative neighbors set with Euclidean distance in observation spaces. Then, the autoencoder is trained by joint minimization of the Bernoulli cross-entropy error between input and output and the sum of the square error between neighbors of input and output. The results of two widely used corpora show that our method yields at least a 15% improvement in document clustering and a nearly 7% improvement in classification tasks compared to comparative methods. The evidence demonstrates that our method can readily capture more discriminative latent representation of new documents. Moreover, some meaningful combinations of words can be efficiently discovered by activating features that promote the comprehensibility of latent representation.
Detecting Lo cal Manifold Structure for Unsup ervised Feature Selection
Institute of Scientific and Technical Information of China (English)
FENG Ding-Cheng; CHEN Feng; XU Wen-Li
2014-01-01
Unsupervised feature selection is fundamental in statistical pattern recognition, and has drawn persistent attention in the past several decades. Recently, much work has shown that feature selection can be formulated as nonlinear dimensionality reduction with discrete constraints. This line of research emphasizes utilizing the manifold learning techniques, where feature selection and learning can be studied based on the manifold assumption in data distribution. Many existing feature selection methods such as Laplacian score, SPEC (spectrum decomposition of graph Laplacian), TR (trace ratio) criterion, MSFS (multi-cluster feature selection) and EVSC (eigenvalue sensitive criterion) apply the basic properties of graph Laplacian, and select the optimal feature subsets which best preserve the manifold structure defined on the graph Laplacian. In this paper, we propose a new feature selection perspective from locally linear embedding (LLE), which is another popular manifold learning method. The main difficulty of using LLE for feature selection is that its optimization involves quadratic programming and eigenvalue decomposition, both of which are continuous procedures and different from discrete feature selection. We prove that the LLE objective can be decomposed with respect to data dimensionalities in the subset selection problem, which also facilitates constructing better coordinates from data using the principal component analysis (PCA) technique. Based on these results, we propose a novel unsupervised feature selection algorithm, called locally linear selection (LLS), to select a feature subset representing the underlying data manifold. The local relationship among samples is computed from the LLE formulation, which is then used to estimate the contribution of each individual feature to the underlying manifold structure. These contributions, represented as LLS scores, are ranked and selected as the candidate solution to feature selection. We further develop a
Study on Vibration Fault diagnosis of Diesel Engine Based on Manifold Learning%基于流形学习的柴油机振动故障诊断方法研究
Institute of Scientific and Technical Information of China (English)
潘永波
2015-01-01
船舶柴油机是一个复杂程度较高的系统,其复杂性的构造和工作原理增加了其产生故障症状的复杂性和故障诊断工作的困难性.一般情况下,船舶柴油机故障原因和故障预兆间呈现出一种错综复杂的非线性关系,且在各个参数间也存在较强的非线性和耦合性,所以,诊断船舶柴油机故障,往往是顺应船舶柴油的这一复杂性结构要求而采用非线性手段对其进行相应的故障诊断和状态监测.流形学习法就是这样一种方法.随着流形学习算法被广泛应用于机械故障诊断领域,其已成为我国模式识别研究领域中的一个热点问题.但目前,流形学习在柴油机故障诊断过程中的应用还存在一定缺陷.本文基于流形学习的基本理论原理进行探讨,并着重对流形学习法在船舶柴油机振动故障诊断方面的应用进行归纳和总结.%Marine diesel engine is a complex system with a high degree of complexity, and the complexity of the structure and working principle of marine diesel engine has increased the complexity and difficulty of fault diagnosis. Under normal circumstances, there is a complicated nonlinear relationship between marine diesel engine fault and fault warning, and there is a strong nonlinear and coupling among the various parameters, so that the fault diagnosis of marine diesel engine is often the fault diagnosis and condition monitoring of the ship diesel engine. Manifold learning method is such a method. With manifold learning algorithm is widely used in the field of mechanical fault diagnosis, it has become a hot issue in the field of pattern recognition. But at present, there are some defects in the application of manifold learning in the process of fault diagnosis of diesel engine. In this paper, the basic theory of manifold learning is discussed, and the application of manifold learning method in vibration fault diagnosis of marine diesel engine is summarized and summarized.
Target detection performed on manifold approximations recovered from hyperspectral data
Ziemann, Amanda K.; Messinger, David W.; Albano, James A.
2013-05-01
In high dimensional data, manifold learning seeks to identify the embedded lower-dimensional, non-linear mani- fold upon which the data lie. This is particularly useful in hyperspectral imagery where inherently m-dimensional data is often sparsely distributed throughout the d-dimensional spectral space, with m << d. By recovering the manifold, inherent structures and relationships within the data - which are not typically apparent otherwise - may be identified and exploited. The sparsity of data within the spectral space can prove challenging for many types of analysis, and in particular with target detection. In this paper, we propose using manifold recovery as a preprocessing step for spectral target detection algorithms. A graph structure is first built upon the data and the transformation into the manifold space is based upon that graph structure. Then, the Adaptive Co- sine/Coherence Estimator (ACE) algorithm is applied. We present an analysis of target detection performance in the manifold space using scene-derived target spectra from two different hyperspectral images.
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
Institute of Scientific and Technical Information of China (English)
汪成龙; 李小昱; 武振中; 周竹; 冯耀泽
2014-01-01
Buds and uneven surface of potatoes have caused problems to detect the mechanical damage based on machine vision. The lighting conditions and gray value changes of defect region have great impacts on the pixel level feature extraction. While manifold learning methods have been extensively studied in the face recognition, they have not been used for the external quality inspection of agricultural products. The manifold learning method is mainly divided into linear and nonlinear manifold learning algorithms. The nonlinear manifold learning algorithm includes isometric mapping (Isomap), locally linear embedding (LLE), laplacian eigenmaping (LE). The linear algorithm is extension of the nonlinear methods such as principal component analysis (PCA) and multidimensional scaling (MDS). In order to weaken the influence of the buds and uneven surface on potatoes mechanical damage detection, the image was characterized by using low dimensional manifolds. A mechanical damage detection method for potatoes was provided based on manifold learning. In this study, the Saliency and H images were firstly segmented on the potato regional image. The segmentation accuracies of both images are 100%. However, Saliency-H method can the potato’s location information of the image by unsupervised pattern was automatically obtained. In addition, Saliency-H method was faster (average elapsed time is 477.7ms) than H method with a high data compression rate. After the potato region images were resampled from 1024×768 to 64×64, the features of potato images were extracted from the resample images by using the three manifold learning methods: principal component analysis (PCA), isometric mapping (Isomap) and locally linear embedding (LLE). Thirdly, the three corresponding SVM classification models were developed based on their features. Finally the parameters of the models were optimized to develop corresponding optimal classification models by using the grid search method (grid search
Energy Technology Data Exchange (ETDEWEB)
Chen Ting; Jabbour, Salma K.; Haffty, Bruce G.; Yue, Ning [Radiation Oncology Department, Cancer Institute of New Jersey, University of Medicine and Dentistry of New Jersey, 195 Little Albany Street, New Brunswick, New Jersey 08901 (United States); Qin Songbing [Department of Radiation Oncology, The First Affiliated Hospital of Soochow University, Suzhou 215006 (China)
2013-04-15
Purpose: The management of thoracic malignancies with radiation therapy is complicated by continuous target motion. In this study, a real time motion analysis approach is proposed to improve the accuracy of patient setup. Methods: For 11 lung cancer patients a long training fluoroscopy was acquired before the first treatment, and multiple short testing fluoroscopies were acquired weekly at the pretreatment patient setup of image guided radiotherapy (IGRT). The data analysis consisted of three steps: first a 4D target motion model was constructed from 4DCT and projected to the training fluoroscopy through deformable registration. Then the manifold learning method was used to construct a 2D subspace based on the target motion (kinetic) and location (static) information in the training fluoroscopy. Thereafter the respiratory phase in the testing fluoroscopy was determined by finding its location in the subspace. Finally, the phase determined testing fluoroscopy was registered to the corresponding 4DCT to derive the pretreatment patient position adjustment for the IGRT. The method was tested on clinical image sets and numerical phantoms. Results: The registration successfully reconstructed the 4D motion model with over 98% volume similarity in 4DCT, and over 95% area similarity in the training fluoroscopy. The machine learning method derived the phase values in over 98% and 93% test images of the phantom and patient images, respectively, with less than 3% phase error. The setup approach achieved an average accumulated setup error less than 1.7 mm in the cranial-caudal direction and less than 1 mm in the transverse plane. All results were validated against the ground truth of manual delineations by an experienced radiation oncologist. The expected total time for the pretreatment setup analysis was less than 10 s. Conclusions: By combining the registration and machine learning, the proposed approach has the potential to improve the accuracy of pretreatment setup for
Institute of Scientific and Technical Information of China (English)
王娜; 李霞; 刘国胜
2012-01-01
Locality preserving manifold learning algorithms always discover intrinsic manifold in high-dimensional data by preserving locality neighborhood structures. However, for high-dimensional data with non-enough training samples, or with nonlinear structure and redundant or interrupted features, it is difficult to directly estimate real neighbor relation defined by Euclidean distance in original feature space. This paper proposed a novel method to find a feature subspace best suited to representing neighborhood relation using positive constraints. In this subspace more inner-class samples come together. Further,constructed neighborhood graph in this subspace to discover intrinsic manifold in high-dimensional data, which caused novel locality preserving manifold learning algorithms called NFS-LPP and NFS-NPE. Experimental results on Yale and ORL face database verify their effectiveness.%局部保持流形学习算法通过保持局部邻域特性来挖掘隐藏在高维数据中的内在流形结构.然而,对于缺乏足够训练样本的高维数据集,或者高维数据集存在非线性结构和高维数据特征中存在冗余、干扰特征,使得在原特征空间中利用欧式距离定义的邻域关系并不能真实反映数据的内在流形结构,从而影响算法的性能.提出利用正约束寻找特征子空间的方法,使得在此子空间中更多的同类样本紧聚,并进一步在该子空间中构建邻域关系来挖掘高维数据的内在流形,形成基于特征子空间邻域特性的局部保持流形学习算法(NFS-LPP和NFS-NPE).它们在一定程度上克服了高维小样本数据集难以正确挖掘内在流形结构的问题,在Yale和ORL人脸库上的分类和聚类实验验证了其有效性.
Manifold traversing as a model for learning control of autonomous robots
Szakaly, Zoltan F.; Schenker, Paul S.
1992-01-01
This paper describes a recipe for the construction of control systems that support complex machines such as multi-limbed/multi-fingered robots. The robot has to execute a task under varying environmental conditions and it has to react reasonably when previously unknown conditions are encountered. Its behavior should be learned and/or trained as opposed to being programmed. The paper describes one possible method for organizing the data that the robot has learned by various means. This framework can accept useful operator input even if it does not fully specify what to do, and can combine knowledge from autonomous, operator assisted and programmed experiences.
Face Recognition Based on LBP and Manifold Learning%一种基于LBP特征与流形知识的人脸识别方法
Institute of Scientific and Technical Information of China (English)
李菱歌; 蔡超
2014-01-01
Face recognition is a hot research topic in the field of computer vision ,and has wide application .Recently manifolds are thought to be fundamental for visual perception ,and manifold learning algorithms are developed for discovering intrinsical features .How to use the low dimensional intrinsic variables obtained by manifold learning becomes the core issue of related research .But the classification result sometimes is not accurate when faces are classified in low dimensional sub-space directly .Furthermore ,manifold learning methods are sensitive to the variation of illumination conditions .In order to solve these two problems ,a novel face recognition method based on LBP and manifold learning is proposed .Firstly ,LBP op-erator is used to describe the local features of the face images .After obtaining the intrinsic variables of the feature data by manifold learning algorithm ,the manifold is then approximated by higher-order Taylor expansion whose parameters are saved as manifold knowledge .And then face recognition is realized by solving the manifold distance .Experimental results show that the proposed method is robust to illumination and can improve face recognition performance effectively .%人脸识别是计算机视觉领域的研究热点，应用背景广泛。近年来，流形被认为是视觉感知的基础，流形学习算法被用来发现图像的内在特征。如何利用流形学习后的低维内蕴变量成为相关研究的核心问题。但是利用传统的流形学习算法降维得到的人脸低维特征在可分性上存在一定的不足。此外，流形学习算法对光照和姿态变化敏感。针对这两个问题，提出了一种基于局部二值模式（LBP）和流形知识的人脸识别方法。该方法首先利用LBP算子对人脸图像进行局部特征描述，然后使用流形学习算法获得高维特征数据的低维内蕴变量，并用泰勒展开式近似该流形，获取流形知识，最后利用流形
Huang, Tao; Li, Xiao-yu; Jin, Rui; Ku, Jing; Xu, Sen-miao; Xu, Meng-ling; Wu, Zhen-zhong; Kong, De-guo
2015-04-01
The present paper put forward a non-destructive detection method which combines semi-transmission hyperspectral imaging technology with manifold learning dimension reduction algorithm and least squares support vector machine (LSSVM) to recognize internal and external defects in potatoes simultaneously. Three hundred fifteen potatoes were bought in farmers market as research object, and semi-transmission hyperspectral image acquisition system was constructed to acquire the hyperspectral images of normal external defects (bud and green rind) and internal defect (hollow heart) potatoes. In order to conform to the actual production, defect part is randomly put right, side and back to the acquisition probe when the hyperspectral images of external defects potatoes are acquired. The average spectrums (390-1,040 nm) were extracted from the region of interests for spectral preprocessing. Then three kinds of manifold learning algorithm were respectively utilized to reduce the dimension of spectrum data, including supervised locally linear embedding (SLLE), locally linear embedding (LLE) and isometric mapping (ISOMAP), the low-dimensional data gotten by manifold learning algorithms is used as model input, Error Correcting Output Code (ECOC) and LSSVM were combined to develop the multi-target classification model. By comparing and analyzing results of the three models, we concluded that SLLE is the optimal manifold learning dimension reduction algorithm, and the SLLE-LSSVM model is determined to get the best recognition rate for recognizing internal and external defects potatoes. For test set data, the single recognition rate of normal, bud, green rind and hollow heart potato reached 96.83%, 86.96%, 86.96% and 95% respectively, and he hybrid recognition rate was 93.02%. The results indicate that combining the semi-transmission hyperspectral imaging technology with SLLE-LSSVM is a feasible qualitative analytical method which can simultaneously recognize the internal and
标架丛上的多流形联络学习算法%Multi-manifold Connection Learning Algorithm Based on Frame Bundle
Institute of Scientific and Technical Information of China (English)
张启明; 李凡长
2015-01-01
Traditional manifold learning methods need a large number of training samples. All samples are regarded as a manifold and then discriminative features are extracted for practical application such as classification. But in many situations, only one sample is existed during the training phase since there are not enough training samples. Therefore, frame bundle connection learning method is presented and a multi-manifold structure is constructed. Besides, intermanifold and intramanifold features are extracted to get more discriminative information to solve the problem. When dealing with the multi-manifold structure, learning models of two subspaces based on frame bundle are used to project the data in high-dimensional space to horizontal space for maximizing margins of different manifolds. Simultaneously, the data structure is maintained with the same manifold in the vertical space. Finally, a simulation experiment is presented to prove the validity of the proposed algorithm.%传统的流形学习算法通常需要较多的训练样本，将所有样本看作一个流形进行学习，并提取判别特征以进行后续的分类等具体应用。然而在很多实际问题中，并不能获得大量的训练样本，因此存在很多只有一个训练样本的情况。文中提出标架丛上联络学习算法，构建出多流形结构，提取出流形与流形间以及单一流形内的判别信息处理样本少的情形。在处理多流形结构数据集时，利用标架丛上的横空间和纵空间学习模型，将高维空间数据投影到横空间以最大化流形与流形间的间隔，同时又在纵空间中保持同一流形内数据的相关结构。最后通过实例验证了本文算法的有效性。
Leff, Daniel Richard; Orihuela-Espina, Felipe; Atallah, Louis; Athanasiou, Thanos; Leong, Julian J H; Darzi, Ara W; Yang, Guang-Zhong
2008-11-01
The prefrontal cortex (PFC) is known to be vital for acquisition of visuomotor skills, but its role in the attainment of complex technical skills which comprise both perceptual and motor components, such as those associated with surgery, remains poorly understood. We hypothesized that the prefrontal response to a surgical knot-tying task would be highly dependent on technical expertise, and that activation would wane in the context of learning success following extended practice. The present series of experiments investigated this issue, using functional Near Infrared Spectroscopy (fNIRS) and dexterity analysis to compare the PFC responses and technical skill of expert and novice surgeons performing a surgical knot-tying task in a block design experiment. Applying a data-embedding technique known as Isomap and Earth Mover's Distance (EMD) analysis, marked differences in cortical hemodynamic responses between expert and novice surgeons have been found. To determine whether refinement in technical skill was associated with reduced PFC demands, a second experiment assessed the impact of pre- and post-training on the PFC responses in novices. Significant improvements (p learning-related refinements in technical performance are mediated by temporal reductions in prefrontal activation.
A framework for optimal kernel-based manifold embedding of medical image data.
Zimmer, Veronika A; Lekadir, Karim; Hoogendoorn, Corné; Frangi, Alejandro F; Piella, Gemma
2015-04-01
Kernel-based dimensionality reduction is a widely used technique in medical image analysis. To fully unravel the underlying nonlinear manifold the selection of an adequate kernel function and of its free parameters is critical. In practice, however, the kernel function is generally chosen as Gaussian or polynomial and such standard kernels might not always be optimal for a given image dataset or application. In this paper, we present a study on the effect of the kernel functions in nonlinear manifold embedding of medical image data. To this end, we first carry out a literature review on existing advanced kernels developed in the statistics, machine learning, and signal processing communities. In addition, we implement kernel-based formulations of well-known nonlinear dimensional reduction techniques such as Isomap and Locally Linear Embedding, thus obtaining a unified framework for manifold embedding using kernels. Subsequently, we present a method to automatically choose a kernel function and its associated parameters from a pool of kernel candidates, with the aim to generate the most optimal manifold embeddings. Furthermore, we show how the calculated selection measures can be extended to take into account the spatial relationships in images, or used to combine several kernels to further improve the embedding results. Experiments are then carried out on various synthetic and phantom datasets for numerical assessment of the methods. Furthermore, the workflow is applied to real data that include brain manifolds and multispectral images to demonstrate the importance of the kernel selection in the analysis of high-dimensional medical images.
Manifold Learning Co-Location Decision Tree for Remotely Sensed Imagery Classification
Directory of Open Access Journals (Sweden)
Guoqing Zhou
2016-10-01
Full Text Available Because traditional decision tree (DT induction methods cannot efficiently take advantage of geospatial knowledge in the classification of remotely sensed imagery, several researchers have presented a co-location decision tree (CL-DT method that combines the co-location technique with the traditional DT method. However, the CL-DT method only considers the Euclidean distance of neighborhood events, which cannot truly reflect the co-location relationship between instances for which there is a nonlinear distribution in a high-dimensional space. For this reason, this paper develops the theory and method for a maximum variance unfolding (MVU-based CL-DT method (known as MVU-based CL-DT, which includes unfolding input data, unfolded distance calculations, MVU-based co-location rule generation, and MVU-based CL-DT generation. The proposed method has been validated by classifying remotely sensed imagery and is compared with four other types of methods, i.e., CL-DT, classification and regression tree (CART, random forests (RFs, and stacked auto-encoders (SAE, whose classification results are taken as “true values.” The experimental results demonstrate that: (1 the relative classification accuracies of the proposed method in three test areas are higher than CL-DT and CART, and are at the same level compared to RFs; and (2 the total number of nodes, the number of leaf nodes, and the number of levels are significantly decreased by the proposed method. The time taken for the data processing, decision tree generation, drawing of the tree, and generation of the rules are also shortened by the proposed method compared to CL-DT, CART, and RFs.
Postoperative 3D spine reconstruction by navigating partitioning manifolds
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Kadoury, Samuel, E-mail: samuel.kadoury@polymtl.ca [Department of Computer and Software Engineering, Ecole Polytechnique Montreal, Montréal, Québec H3C 3A7 (Canada); Labelle, Hubert, E-mail: hubert.labelle@recherche-ste-justine.qc.ca; Parent, Stefan, E-mail: stefan.parent@umontreal.ca [CHU Sainte-Justine Hospital Research Center, Montréal, Québec H3T 1C5 (Canada)
2016-03-15
Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.
Differential Calculus on N-Graded Manifolds
Directory of Open Access Journals (Sweden)
G. Sardanashvily
2017-01-01
Full Text Available The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a smooth manifold Z. A key point is that the graded derivation module of the structure ring of graded functions on an N-graded manifold is the structure ring of global sections of a certain smooth vector bundle over its body Z. Accordingly, the Chevalley–Eilenberg differential calculus on an N-graded manifold provides it with the de Rham complex of graded differential forms. This fact enables us to extend the differential calculus on N-graded manifolds to formalism of nonlinear differential operators, by analogy with that on smooth manifolds, in terms of graded jet manifolds of N-graded bundles.
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
Manifold knowledge extraction and target recognition
Chao, Cai; Hua, Zhou
2009-10-01
Advanced mammalian target identification derived from the perception of target's manifold and measurement manifolddistance. It does not rely on object's segmented accuracy, not depend on target's variety model, and adapt to a range of changes on targets. In this paper, based on the existed manifold learning algorithm, set up a new bionic automatic target recognition model, discussed the targets manifold knowledge acquisition and the knowledge expression architecture, gave a manifold knowledge-based new method for automatic target recognition. Experiments show that the new method has a strong adaptability to targets various transform, and has a very high correctly identification probability.
Individualized Learning Through Non-Linear use of Learning Objects: With Examples From Math and Stat
DEFF Research Database (Denmark)
Rootzén, Helle
2015-01-01
Our aim is to ensure individualized learning that is fun, inspiring and innovative. We believe that when you enjoy, your brain will open up and learning will be easier and more effective. The methods use a non-linear learning environment based on self-contained learning objects which are pieced t...
Linear low-rank approximation and nonlinear dimensionality reduction
Institute of Scientific and Technical Information of China (English)
ZHANG Zhenyue; ZHA Hongyuan
2004-01-01
We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.
Manifold Learning and Its Application in Retrieval%流形学习及其在检索中的应用
Institute of Scientific and Technical Information of China (English)
邢芝会; 孙建德
2011-01-01
As a new unsupervised learning method, manifold learning has captured the attention of researchers in the field of machine learning and cognitive science. Its nature is to find the relation between intrinsic low-dimensional manifold structure and embedded mapping in the high-dimensional observed data set. Many algorithms in manifold learning have been study hotspot and widely applied in image information compression, pattern recognition and image processing. This paper mainly illustrates the research background, each algorithm's description in math, the application in image and video retrieval, and the future study direction of manifold learning.%作为一种新的非监督性统计学习方法，流形学习近年来越来越引起机器学习及认知科学工作者的重视。其本质是发现高维观测数据集的内在低维流形结构和嵌入映射关系。流形学习的各种算法也成为研究热点，很多经典流形学习算法包括多维尺度分析（Multidimensional Scaling, MDS）、主成分分析（Principle Component Analysis, PCA）、拉普拉斯特征变换（Laplacian Eigenmaps, LE）、局部线性嵌入（Locally Linear Embedding, LLE）、等度规映射（Isometric Mapping, Isomap）等在图像信息压缩、模式识别、图像处理等众多领域都有广泛应用。本文主要介绍了流形学习的研究背景，各个算法的数学描述，在图像视频检索领域的应用以及未来的研究方向。
Discriminant Manifold Learning Approach for Hyperspectral Image Dimension Reduction%高光谱图像降维的判别流形学习方法
Institute of Scientific and Technical Information of China (English)
杜博; 张乐飞; 张良培; 胡文斌
2013-01-01
A discriminant manifold learning approach for hyperspectral image dimension reduction was proposed. In order to overcome the high dimensional and high redundancy of remotely sensed earth observation images, a modified manifold learning algorithm was suggested for dataset linear dimensional reduction to improve the performance of image classification. The proposed method addressed the discriminative information of given training samples into the current manifold learning framework to learn an optimal subspace for subsequent classification, in particular, the linearization of discriminant manifold learning is introduced to deal with the out of sample problem. Experiments on hyperspectral image demonstrated that the proposed method could achieve higher classification rate than the conventional image classification technologies.%本文提出了一种高光谱图像降维的判别流形学习方法.针对获取的大量遥感对地观测数据存在大量冗余信息的特点,引入改进的流形学习方法对高光谱遥感数据进行降维处理,以提高遥感图像自动分类的总体准确度.该方法充分利用遥感图像自动分类中训练样本的判别信息,将输入样本的类别信息加入到常规流形学习方法的框架中,从本质上提高输出的特征在低维空间中的判别力.同时,引入线性化模型以解决流形学习方法中常见的小样本问题.对高光谱遥感图像自动分类的实验表明,基于判别流形学习的高光谱遥感图像自动分类方法能够显著地提高图像分类准确度.
Nonlinear Connection in Grassmannian Manifold Gr （2 ＋ 1, 2）%Grassmann流形Gr（2＋1，2）上的非线性联络
Institute of Scientific and Technical Information of China (English)
何建新
2012-01-01
In this article, conceptions and relative theorems of Grassmannian manifold and connection of prin- cipal fiber bundle were introduced. Compute the nonlinear connection of fiber bundle was calculated, in which fiber is Gr （2＋1, 2）.%本文介绍了Grassmann流形、主纤维丛联络的相关概念和定理，计算了以Gr（2＋1，2）为纤维形上的非线性联络。
Compressive sensing reconstruction method based on parametric manifold learning%基于参数化流形学习的压缩传感重构方法
Institute of Scientific and Technical Information of China (English)
宫磊; 赵方; 陆阳
2012-01-01
Compressive sensing is a new theory of information acquisition, which breaks through the traditional sampling theory. It combines data acquisition with data compression, and then recovers the original signal by reconstruction algorithms. In order to get the better effect of compressive sensing construction, this paper mainly combined the ideas and methods of manifold learning with compressive sensing, and then proposed a compressive sensing reconstruction method based on parametric manifold learning. The experimental results show that reconstruction of natural images has very good results with the proposed method. Therefore, it fully verifies the effectiveness of compressive sensing reconstruction method based on parametric manifold learning.%压缩传感是一种新的信息获取理论,它突破了传统的采样理论,将数据采集和压缩合二为一,再利用重构算法将原始数据恢复.为了能够得到更好的压缩传感重构效果,把流形学习的思想和方法与压缩传感相结合,提出了一种基于参数化流形学习的压缩传感重构方法.实验结果表明,提出的方法对自然图像进行重构取得了很好的效果,充分验证了基于参数化流形学习的压缩传感重构方法的有效性.
MADMM: a generic algorithm for non-smooth optimization on manifolds
Kovnatsky, Artiom; Glashoff, Klaus; Bronstein, Michael M.
2015-01-01
Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems and show its application to several challenging problems in dimensionality reduction, data analysis, and manifold learning.
基于半监督流形学习的人脸识别方法%Face Recognition Based on Semi-supervised Manifold Learning
Institute of Scientific and Technical Information of China (English)
黄鸿; 李见为; 冯海亮
2008-01-01
如何有效地将流形学习(Manifold learning,ML)和半监督学习(Semi-supervised learning,SSL)方法进行结合是近年来模式识别和机器学习领域研究的热点问题.提出一种基于半监督流形学习(Semi-supervised manifold learning,SSML)的人脸识别方法,它在部分有标签信息的人脸数据的情况下,通过利用人脸数据本身的非线性流形结构信息和部分标签信息来调整点与点之间的距离形成距离矩阵,而后基于被调整的距离矩阵进行线性近邻重建来实现维数约简,提取低维鉴别特征用于人脸识别.基于公开的人脸数据库上的实验结果表明,该方法能有效地提高人脸识别的性能.
Institute of Scientific and Technical Information of China (English)
李国芳
2014-01-01
Face-image feature extraction is one of the key technologies and problems in face recognition systems. Manifold learn⁃ing algorithm, as a non-linear dimension reduction method, has been used in facial recognition field and speech recognition field in recent years. A new feature extraction based on 2DPCA(Two-Dimentional PCA) and LPP(Locality Preserving Projections) al⁃gorithm of the manifold learning is proposed through systematic study of facial recognition system. And it may provide a good ref⁃erence for further study of facial recognition technology. The simulation experiment shows that this algorithm has better recogni⁃tion rate as compared with PCA, LDA algorithms of traditional feature extraction.%人脸图像的特征提取是人脸识别系统中最关键同时也是难题之一。流形学习算法是近些年的人脸识别和语音识别两个领域应用较多的非线性降维方法。通过对人脸识别系统的研究，现提出一种全新的基于2DPCA(Two-Dimentional PCA)和流形学习LPP(Locality Preserving Projections)算法的特征提取方法，可为今后深入研究人脸识别技术提供较好的参考。仿真实验表明，该算法与传统特征提取PCA、LDA算法相比，可以取得更好的识别率。
Research of a manifold learning algorithm based on spectral clustering%基于谱聚类的流形学习算法研究
Institute of Scientific and Technical Information of China (English)
王洪波; 罗贺
2013-01-01
传统流形学习算法虽然是一种常用的有效降维方法,但由于其自身计算结构的限制,往往存在数据分析不足和计算时间较长等问题.为此提出一种基于谱聚类的流形学习算法(spectral clustering locally linear embedding,SCLLE),并对其机理以及优点给予了实例证明.在UCI和NCBI数据集上的实验结果表明,该算法具有较好的识别效果和计算性能.%Although traditional manifold learning algorithms are common and effective dimension reduction methods, they still have calculating structure limits of their own, which lead to some problems such as inadequate data analyses and long calculation time. Therefore, on the basis of spectral clustering, a manifold learning algorithm named SCLLE (spectral clustering locally linear embedding) was proposed and its mechanisms as well as its advantages were demonstrated. Experiments with UCI and NCBI data sets show that the proposed algorithm has better recognition effect and computational performance.
Renteln, Paul
2013-11-01
Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
Funar, L
1995-01-01
The aim of this note is to derive some invariants at infinity for open 3-manifolds in the framework of Topological Quantum Field Theories. These invariants may be used to test if an open manifold is simply connected at infinity as we done for Whitehead's manifold in case of the sl_{2}({\\bf C})-TQFT in level 4.
基于自组织映射的流形学习与可视化%Manifold learning and visualization based on serf-organizing map
Institute of Scientific and Technical Information of China (English)
邵超; 万春红
2013-01-01
针对自组织映射(SOM)在学习和可视化高维数据内在的低维流形结构时容易产生“拓扑缺陷”的这一问题,提出了一种新的流形学习算法——动态自组织映射(DSOM).该算法按照数据的邻域结构逐步扩展训练数据集合,对网络进行渐进训练,以避免局部极值,克服“拓扑缺陷”问题；同时,网络规模也随之动态扩展,以降低算法的时间复杂度.实验表明,该算法能更加真实地学习和可视化高维数据内在的低维流形结构；此外,与传统的流形学习算法相比,该算法对邻域大小和噪声也更加鲁棒.所提算法的网络规模和训练数据集合都将按照数据内在的邻域结构进行同步扩展,从而能更加简洁并真实地学习和可视化高维数据内在的低维流形结构.%Self-Organizing Map (SOM) tends to yield the topological defect problem when learning and visualizing the intrinsic low-dimensional manifold structure of high-dimensional data sets.To solve this problem,a manifold learning algorithm,Dynamic Self-Organizing MAP (DSOM),was presented in this paper.In the DSOM,the training data set was expanded gradually according to its neighborhood structure,and thus the map was trained step by step,by which local minima could be avoided and the topological defect problem could be overcome.Meanwhile,the map size was increased dynamically,by which the time cost of the algorithm could be reduced greatly.The experimental results show that DSOM can learn and visualize the intrinsic low-dimensional manifold structure of high-dimensional data sets more faithfully than SOM.In addition,compared with traditional manifold learning algorithms,DSOM can obtain more concise visualization results and be less sensitive to the neighborhood size and the noise,which can also be verified by the experimental results.The innovation of this paper lies in that DSOM expands the map size and the training data set synchronously according to its
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.
2013-09-26
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Study of Image Dimensional Reduction Algorithm Based on Manifold Learning%基于流形学习的图像降维算法研究
Institute of Scientific and Technical Information of China (English)
侯远韶
2015-01-01
One-dimensional and two-dimensional image feature extraction ignores the image structure information,which will result in the loss of recognition accuracy.Three-dimensional and multi-dimensional image feature extraction considers the links between each data structure,however it brings the curse of dimensionality,which will increase the computational complexity.Accordingly,in this paper,manifold learning is taken to embed a stable manifold in the original data space,thus the multi-dimensional data feature data can be mapped to the manifold,the invisible low-dimensional structure implicated in the high-dimensional data sets can be perceived, the original data dimension can be reduced without losing data,and thereby the computational complexity can be reduced.%传统的一维、二维图像特征提取忽略了图像的结构信息，由此带来识别精度的损失；三维和多维图像的特征提取虽然考虑了数据结构之间的彼此联系，但却带来了维数灾难，增加了计算复杂度。本文利用流形学习，在原始的数据空间中嵌入稳定的流形，从而使多维数据中的特征数据映射到流形上，发现隐含在高维数据集中人们无法感知的低维结构，在不丢失数据信息的前提下，降低原始数据的维数，从而降低计算复杂度。
Institute of Scientific and Technical Information of China (English)
刘坤; 李飚; 曾祥鑫
2015-01-01
太赫兹时域光谱技术是一门新兴光谱检测技术,广泛应用于安检及反恐、生物医学和食品质量检测等方面.太赫兹谱的分类识别技术是太赫兹光谱检测技术的一个重要环节.由于受到噪声的影响,太赫兹谱可能在高维空间中成复杂的非线性分布,传统的分类方法难以取得理想的分类效果.流形学习和支持向量机都是当前机器学习领域的研究热点,都采取了核方法来解决非线性问题,正因为两者之间有很多共通之处,将这两种方法充分结合提出了一种称之为ISOMAP-SVM的新算法.这种新算法拥有比传统的支持向量机算法更快的训练速度和更好的分类效果.实验结果表明利用新算法可以实现对不同种类药品的识别,为太赫兹光谱技术用于药品的检测和识别提供了一种新的有效方法.%Terahertz time-domain spectroscopy is a new spectrum detection technology, and applied to various research fields:national security and defense, biomedical and food quality inspection. The classification of THz spectrums is one crucial domain of THz measurement. Because of the influence of noise, the result of traditional pattern classification methods is not satisfactory. Manifold learning and SVM are both effective approaches for non-linear pattern analysis problems and are also new research focus in current machine learning community. A new algorithm based on manifold learning and SVM is proposed in this paper. Compared to traditional SVM, this algorithm can improve the classification performance of SVM. Experimental result demonstrates that this algorithm can be applied to medical identification. It provides an effec-tive method for the detection and identification of medical by terahertz spectroscopy technology.
Complex synchronization manifold in coupled time-delayed systems
Energy Technology Data Exchange (ETDEWEB)
Hoang, Thang Manh, E-mail: hmt@mail.hut.edu.v [Signal and Information Processing Laboratory, Faculty of Electronics and Telecommunications, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi (Viet Nam)
2011-01-15
Research highlights: The complex synchronization manifold in coupled multiple time delay systems is demonstrated for the first time. The complex synchronization manifold is in the form of sum of multiple simple manifolds. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. - Abstract: In the present paper, the complex synchronization manifold generated in coupled multiple time delay systems is demonstrated for the first time. There, the manifold is in the form of sum of multiple simple manifolds. The structure of master is identical to that of slave. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. The specific examples will demonstrate and verify the effectiveness of the proposed model.
Radio Interferometric Calibration Using a Riemannian Manifold
Yatawatta, Sarod
2013-01-01
In order to cope with the increased data volumes generated by modern radio interferometers such as LOFAR (Low Frequency Array) or SKA (Square Kilometre Array), fast and efficient calibration algorithms are essential. Traditional radio interferometric calibration is performed using nonlinear optimization techniques such as the Levenberg-Marquardt algorithm in Euclidean space. In this paper, we reformulate radio interferometric calibration as a nonlinear optimization problem on a Riemannian manifold. The reformulated calibration problem is solved using the Riemannian trust-region method. We show that calibration on a Riemannian manifold has faster convergence with reduced computational cost compared to conventional calibration in Euclidean space.
Inertial manifold of the atmospheric equations
Institute of Scientific and Technical Information of China (English)
李建平; 丑纪范
1999-01-01
For a class of nonlinear evolution equations, their global attractors are studied and the existence of their inertial manifolds is discussed using the truncated method. Then, on the basis of the properties of operators of the atmospheric equations, it is proved that the operator equation of the atmospheric motion with dissipation and external forcing belongs to the class of nonlinear evolution equations. Therefore, it is known that there exists an inertial manifold of the atmospheric equations if the spectral gap condition for the dissipation operator is satisfied. These results furnish a basis for further studying the dynamical properties of global attractor of the atmospheric equations and for designing better numerical scheme.
Symmetries from the solution manifold
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Huang, Anpeng; Xu, Wenyao; Li, Zhinan; Xie, Linzhen; Sarrafzadeh, Majid; Li, Xiaoming; Cong, Jason
2014-09-01
Cardiovascular disease (CVD) is a major issue to public health. It contributes 41% to the Chinese death rate each year. This huge loss encouraged us to develop a Wearable Efficient teleCARdiology systEm (WE-CARE) for early warning and prevention of CVD risks in real time. WE-CARE is expected to work 24/7 online for mobile health (mHealth) applications. Unfortunately, this purpose is often disrupted in system experiments and clinical trials, even if related enabling technologies work properly. This phenomenon is rooted in the overload issue of complex Electrocardiogram (ECG) data in terms of system integration. In this study, our main objective is to get a system light-loading technology to enable mHealth with a benchmarked ECG anomaly recognition rate. To achieve this objective, we propose an approach to purify clinical features from ECG raw data based on manifold learning, called the Manifold-based ECG-feature Purification algorithm. Our clinical trials verify that our proposal can detect anomalies with a recognition rate of up to 94% which is highly valuable in daily public health-risk alert applications based on clinical criteria. Most importantly, the experiment results demonstrate that the WE-CARE system enabled by our proposal can enhance system reliability by at least two times and reduce false negative rates to 0.76%, and extend the battery life by 40.54%, in the system integration level.
Distributed Extreme Learning Machine for Nonlinear Learning over Network
Songyan Huang; Chunguang Li
2015-01-01
Distributed data collection and analysis over a network are ubiquitous, especially over a wireless sensor network (WSN). To our knowledge, the data model used in most of the distributed algorithms is linear. However, in real applications, the linearity of systems is not always guaranteed. In nonlinear cases, the single hidden layer feedforward neural network (SLFN) with radial basis function (RBF) hidden neurons has the ability to approximate any continuous functions and, thus, may be used as...
流形学习算法中的参数选择问题研究%ON PARAMETER SELECTION IN MANIFOLD LEARNING ALGORITHM
Institute of Scientific and Technical Information of China (English)
王泽杰; 胡浩民
2010-01-01
流形学习(Manifold Learning)算法是近年来发展起来的非线性降维机器学习算法.等度规特征映射Isomap(Isometric feature mapping)和局部线性嵌入LLE(Locally Linear Embedding)是两种典型的流形学习算法.通过实验比较和分析两种算法中邻接参数K和采样点数N的选取对降维结果以及执行时间的影响,实验结果表明Isomap对邻接参数K和采样点数N具有较高的容忍度,而LLE算法在计算速度上优势明显.
基于局部平滑性的通用增量流形学习算法%Generalized incremental manifold learning algorithm based on local smoothness
Institute of Scientific and Technical Information of China (English)
周雪燕; 韩建敏; 詹宇斌
2012-01-01
Most of the existing manifold learning algorithms are not capable of dealing with new arrival samples. Although some incremental algorithms are developed via extending a specified manifold learning algorithm, most of them have some disadvantages more or less. In this paper, a new and more Generalized Incremental Manifold Learning ( G1ML) algorithm based on local smoothness was proposed. CIML algorithm firstly extracted the local smooth structure of data set via local Principal Component Analysis (PCA). Then the optimal linear transformation, which transformed the local smooth structure of new arrival sample' s neighborhood to its correspondent low-dimensional embedding coordinates, was computed. Finally the low-dimensional embedding coordinates of new arrival samples were obtained by the optimal transformation. Extensive and systematic experiments were conducted on both artificial and real image data sets. The experimental results demonstrate that the GIML algorithm is an effective incremental manifold learning algorithm and outperforms other existing algorithms.%目前大多数流形学习算法无法获取高维输入空间到低维嵌入空间的映射,无法处理新增数据,因此无增量学习能力.而已有的增量流形学习算法大多是通过扩展某一特定的流形学习算法使其具备增量学习能力,不具有通用性.针对这一问题,提出了一种通用的增量流形学习(GIML)算法.该方法充分考虑流形的局部平滑性这一本质特征,利用局部主成分分析法来提取数据集的局部平滑结构,并寻找包含新增样本点的局部平滑结构到对应训练数据的低维嵌入坐标的最佳变换.最后GIML算法利用该变换计算新增样本点的低维嵌入坐标.在人工数据集和实际图像数据集上进行了系统而广泛的比较实验,实验结果表明GIML算法是一种高效通用的增量流形学习方法,且相比当前主要的增量算法,能更精确地获取增量数据的低维嵌入坐标.
Sparks, Rachel; Madabhushi, Anant
2016-06-06
Content-based image retrieval (CBIR) retrieves database images most similar to the query image by (1) extracting quantitative image descriptors and (2) calculating similarity between database and query image descriptors. Recently, manifold learning (ML) has been used to perform CBIR in a low dimensional representation of the high dimensional image descriptor space to avoid the curse of dimensionality. ML schemes are computationally expensive, requiring an eigenvalue decomposition (EVD) for every new query image to learn its low dimensional representation. We present out-of-sample extrapolation utilizing semi-supervised ML (OSE-SSL) to learn the low dimensional representation without recomputing the EVD for each query image. OSE-SSL incorporates semantic information, partial class label, into a ML scheme such that the low dimensional representation co-localizes semantically similar images. In the context of prostate histopathology, gland morphology is an integral component of the Gleason score which enables discrimination between prostate cancer aggressiveness. Images are represented by shape features extracted from the prostate gland. CBIR with OSE-SSL for prostate histology obtained from 58 patient studies, yielded an area under the precision recall curve (AUPRC) of 0.53 ± 0.03 comparatively a CBIR with Principal Component Analysis (PCA) to learn a low dimensional space yielded an AUPRC of 0.44 ± 0.01.
Borok, S.; Goldfarb, I.; Gol'dshtein, V.
2009-05-01
The paper concerns intrinsic low-dimensional manifold (ILDM) method suggested in [Maas U, Pope SB. Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space, combustion and flame 1992;88:239-64] for dimension reduction of models describing kinetic processes. It has been shown in a number of publications [Goldfarb I, Gol'dshtein V, Maas U. Comparative analysis of two asymptotic approaches based on integral manifolds. IMA J Appl Math 2004;69:353-74; Kaper HG, Kaper TJ, Asymptotic analysis of two reduction methods for systems of chemical reactions. Phys D 2002;165(1-2):66-93; Rhodes C, Morari M, Wiggins S. Identification of the low order manifolds: validating the algorithm of Maas and Pope. Chaos 1999;9(1):108-23] that the ILDM-method works successfully and the intrinsic low-dimensional manifolds belong to a small vicinity of invariant slow manifolds. The ILDM-method has a number of disadvantages. One of them is appearance of so-called "ghost"-manifolds, which do not have connection to the system dynamics [Borok S, Goldfarb I, Gol'dshtein V. "Ghost" ILDM - manifolds and their discrimination. In: Twentieth Annual Symposium of the Israel Section of the Combustion Institute, Beer-Sheva, Israel; 2004. p. 55-7; Borok S, Goldfarb I, Gol'dshtein V. About non-coincidence of invariant manifolds and intrinsic low-dimensional manifolds (ILDM). CNSNS 2008;71:1029-38; Borok S, Goldfarb I, Gol'dshtein V, Maas U. In: Gorban AN, Kazantzis N, Kevrekidis YG, Ottinger HC, Theodoropoulos C, editors. "Ghost" ILDM-manifolds and their identification: model reduction and coarse-graining approaches for multiscale phenomena. Berlin-Heidelberg-New York: Springer; 2006. p. 55-80; Borok S, Goldfarb I, Gol'dshtein V. On a modified version of ILDM method and its asymptotic analysis. IJPAM 2008; 44(1): 125-50; Bykov V, Goldfarb I, Gol'dshtein V, Maas U. On a modified version of ILDM approach: asymptotic analysis based on integral manifolds. IMA J Appl Math 2006
Machine learning control taming nonlinear dynamics and turbulence
Duriez, Thomas; Noack, Bernd R
2017-01-01
This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...
BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS
Institute of Scientific and Technical Information of China (English)
钟同德; 钟春平
2003-01-01
Using non-linear connection of Finsler manifold M, the existence of localcoordinates which is normalized at a point x is proved, and the Laplace operator △ on1-form of M is defined by non-linear connection and its curvature tensor. After proving themaximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theoremof Killing vectors and harmonic 1-form are obtained.
Nonlinear programming for classification problems in machine learning
Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio
2016-10-01
We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.
Hildebrand, Richard J.; Wozniak, John J.
2001-01-01
A compressed gas storage cell interconnecting manifold including a thermally activated pressure relief device, a manual safety shut-off valve, and a port for connecting the compressed gas storage cells to a motor vehicle power source and to a refueling adapter. The manifold is mechanically and pneumatically connected to a compressed gas storage cell by a bolt including a gas passage therein.
Particle Filtering on the Audio Localization Manifold
Ettinger, Evan
2010-01-01
We present a novel particle filtering algorithm for tracking a moving sound source using a microphone array. If there are N microphones in the array, we track all $N \\choose 2$ delays with a single particle filter over time. Since it is known that tracking in high dimensions is rife with difficulties, we instead integrate into our particle filter a model of the low dimensional manifold that these delays lie on. Our manifold model is based off of work on modeling low dimensional manifolds via random projection trees [1]. In addition, we also introduce a new weighting scheme to our particle filtering algorithm based on recent advancements in online learning. We show that our novel TDOA tracking algorithm that integrates a manifold model can greatly outperform standard particle filters on this audio tracking task.
Moving Manifolds in Electromagnetic Fields
Directory of Open Access Journals (Sweden)
David V. Svintradze
2017-08-01
Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.
Generalized nonuniform dichotomies and local stable manifolds
Bento, António J G
2010-01-01
We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.
Sensitive Periods in Affective Development: Nonlinear Maturation of Fear Learning
Hartley, Catherine A; Lee, Francis S
2015-01-01
At specific maturational stages, neural circuits enter sensitive periods of heightened plasticity, during which the development of both brain and behavior are highly receptive to particular experiential information. A relatively advanced understanding of the regulatory mechanisms governing the initiation, closure, and reinstatement of sensitive period plasticity has emerged from extensive research examining the development of the visual system. In this article, we discuss a large body of work characterizing the pronounced nonlinear changes in fear learning and extinction that occur from childhood through adulthood, and their underlying neural substrates. We draw upon the model of sensitive period regulation within the visual system, and present burgeoning evidence suggesting that parallel mechanisms may regulate the qualitative changes in fear learning across development. PMID:25035083
利用流形学习进行空间信息服务分类%Research on Geo-spatial Web Services Classification Based on Manifold Learning
Institute of Scientific and Technical Information of China (English)
陈科; 王家耀; 成毅; 谢明霞
2013-01-01
The problems existed in the traditional methods of Web services classification are analyzed, the concepts of manifold and manifold learning and the purpose of introducing the manifold learning into the Web services are described. The algorithm for the visualization and classification of geo-spatial Web services(GWS) based on manifold learning is proposed. During the process of dimension reduction, the similarity between GWS is preserved and the data manifold is unrolled. In order to improve the precision of classification, we gain the mapping rule from the GWS to the 2D data and the initial number of clusters according to the visualization of 2D mapping data. The experimental results prove the validity of the improved visualization and classification algorithm for GWS proposed in this paper.%对现有的Web服务分类方法中存在的问题进行了分析,阐述了流形和流形学习的概念以及将流形学习引入到Web服务领域的目的,提出了利用流形学习进行空间信息服务分类的方法.该方法在空间信息服务降维前后保持各服务间的相似(近邻)关系不变,并通过对服务进行降维可视化指导,确定初始聚类数和聚类中心,从而提高利用聚类分析实现空间信息服务无监督分类的精度.实验表明,本文方法不仅能够对抽象的Web服务进行数值化表示,而且能够有效地提高服务分类的性能.
Parekh, Vishwa S.; Jacobs, Jeremy R.; Jacobs, Michael A.
2014-03-01
The evaluation and treatment of acute cerebral ischemia requires a technique that can determine the total area of tissue at risk for infarction using diagnostic magnetic resonance imaging (MRI) sequences. Typical MRI data sets consist of T1- and T2-weighted imaging (T1WI, T2WI) along with advanced MRI parameters of diffusion-weighted imaging (DWI) and perfusion weighted imaging (PWI) methods. Each of these parameters has distinct radiological-pathological meaning. For example, DWI interrogates the movement of water in the tissue and PWI gives an estimate of the blood flow, both are critical measures during the evolution of stroke. In order to integrate these data and give an estimate of the tissue at risk or damaged; we have developed advanced machine learning methods based on unsupervised non-linear dimensionality reduction (NLDR) techniques. NLDR methods are a class of algorithms that uses mathematically defined manifolds for statistical sampling of multidimensional classes to generate a discrimination rule of guaranteed statistical accuracy and they can generate a two- or three-dimensional map, which represents the prominent structures of the data and provides an embedded image of meaningful low-dimensional structures hidden in their high-dimensional observations. In this manuscript, we develop NLDR methods on high dimensional MRI data sets of preclinical animals and clinical patients with stroke. On analyzing the performance of these methods, we observed that there was a high of similarity between multiparametric embedded images from NLDR methods and the ADC map and perfusion map. It was also observed that embedded scattergram of abnormal (infarcted or at risk) tissue can be visualized and provides a mechanism for automatic methods to delineate potential stroke volumes and early tissue at risk.
Munkres, James R
1997-01-01
A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.
Subspaces indexing model on Grassmann manifold for image search.
Wang, Xinchao; Li, Zhu; Tao, Dacheng
2011-09-01
Conventional linear subspace learning methods like principal component analysis (PCA), linear discriminant analysis (LDA) derive subspaces from the whole data set. These approaches have limitations in the sense that they are linear while the data distribution we are trying to model is typically nonlinear. Moreover, these algorithms fail to incorporate local variations of the intrinsic sample distribution manifold. Therefore, these algorithms are ineffective when applied on large scale datasets. Kernel versions of these approaches can alleviate the problem to certain degree but face a serious computational challenge when data set is large, where the computing involves Eigen/QP problems of size N × N. When N is large, kernel versions are not computationally practical. To tackle the aforementioned problems and improve recognition/searching performance, especially on large scale image datasets, we propose a novel local subspace indexing model for image search termed Subspace Indexing Model on Grassmann Manifold (SIM-GM). SIM-GM partitions the global space into local patches with a hierarchical structure; the global model is, therefore, approximated by piece-wise linear local subspace models. By further applying the Grassmann manifold distance, SIM-GM is able to organize localized models into a hierarchy of indexed structure, and allow fast query selection of the optimal ones for classification. Our proposed SIM-GM enjoys a number of merits: 1) it is able to deal with a large number of training samples efficiently; 2) it is a query-driven approach, i.e., it is able to return an effective local space model, so the recognition performance could be significantly improved; 3) it is a common framework, which can incorporate many learning algorithms. Theoretical analysis and extensive experimental results confirm the validity of this model.
Institute of Scientific and Technical Information of China (English)
赵媛媛; 王力
2014-01-01
The paper prefers to study speech feature extraction based on ISOP manifold learning algorithm. The research attempts to apply ISOP manifold learning algorithm to the model of speech recognition feature extraction. Simulation experiments results show that the proposed algorithm can get a higher recognition rate than the traditional feature extraction algorithm , such as MFCC, LPCC etc.%主要研究了基于流形学习 ISOP 算法的语音特征提取。将流形学习 ISOP 算法应用到语音识别特征提取模块中。仿真实验结果表明，该算法与传统的特征提取算法 MFCC、LPCC 等相比，可以取得较高的识别率。
Joyce, Dominic
2009-01-01
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curv...
Institute of Scientific and Technical Information of China (English)
刘元; 吴小俊
2015-01-01
In image recognition applications, Riemannian manifold learning algorithms can not eliminate the redundant information in images effectively. Therefore, an image recognition algorithm based on Log-Gabor wavelet and Riemannian manifold learning is presented. Firstly, images are processed by the Log-Gabor filter to obtain high-dimensional Log-Gabor image features. Then, the Riemannian manifold learning algorithm is used to reduce the dimensionality of the image features. Research shows that the integration of Log-Gabor wavelet and Riemannian manifold learning is in accord with the process of human visual perception. The proposed algorithm has better robustness to illumination and angle variation of the image. Experimental results on several standard databases indicate the effectiveness of the proposed algorithm.%在图像识别的研究中,黎曼流形学习不能有效消除图像中的冗余信息。基于上述原因,文中提出基于 Log-Gabor 滤波与黎曼流形学习的图像识别算法。首先使用 Log-Gabor 滤波器处理图像,获得维数较高的 Log-Gabor 图像特征,然后使用黎曼流形学习降维图像特征。研究表明,Log-Gabor 滤波与黎曼流形学习的融合算法符合人类视觉感知的过程。文中算法对于光照、角度变化具有较好的鲁棒性,在多个标准数据库上的仿真实验验证文中算法的有效性。
基于流形学习的混合光谱解混分析%Analysis on spectral unmixing based on manifold learning
Institute of Scientific and Technical Information of China (English)
丁玲; 唐娉; 李宏益
2013-01-01
光谱解混分析的重要研究内容是计算分析各地物类别成分在混合像素内所占的比例技术。文中以实测高光谱数据为研究对象，针对高光谱数据具有高维度数、严重的光谱混合等特点，基于流形学习中局部线性嵌入(LLE)算法的思想，提出了一种约束最小乘方局部线性加权回归(CLS-LLWR)建模方法。通过4种典型地物的光谱吸收特征差异分析，从它们不同比例组合下的实测混合光谱中选取了不同波段范围，分别对该模型预测覆盖度信息能力进行了验证分析。最后，将CLS-LLWR模型与主成分回归(PCR)和偏最小二乘回归(PLSR)模型,通过计算预测标准误差(SE)进行了对比分析。结果表明，CLS-LLWR模型有较好的预测能力。这为流形学习在高光谱遥感图像信息提取方面进行了有意的探索。%The main study on spectral unmixing is to develop a regression between mixed spectral features of main land-cover types and their responding fractional cover. Studying on in situ spectral reflectance data, based on one of the best known algorithms of manifold learning, locally linear embedding (LLE), a new modeling method named constrained least squares locally linear weighted regression (CLS-LLWR) was proposed. Spectral reflectance of four kinds of the mixed land-cover types in different percentages was measured and preliminarily analyzed. The model CLS-LLWR was verified by predicting fractional cover of main land- cover types. Compared with principal component regression (PCR) and partial least squares regression (PLSR), through comparison and analysis of the standard error of prediction(SE), the result shows that the CLS-LLWR has better predictability. This study indicates that manifold study has the potential for the information extraction of mixed land cover types in hyperspectral image.
Institute of Scientific and Technical Information of China (English)
刘辉; 杨俊安; 王一
2011-01-01
为解决目前声目标识别面临的鲁棒性不足问题，提出将流形学习应用到声目标的特征提取中，在经典流形学习算法的基础上，研究讨论了目标声信号频域中存在的低维流形，通过两种实际的地面和低空飞行声目标数据集进行对比识别实验，分析了基于流形学习的声目标特征提取方法的性能，结果表明基于流形学习的特征提取方法可以发现声信号的本质特征，提高了声目标识别系统的准确性和鲁棒性．%In order to overcome the deficiency of robustness of low altitude passive acoustic target recognition, the manifold learning is applied to the feature extraction of acoustic targets. Based on the classical algorithm of manifold learning, in the paper we study and discuss the low-dimensional manifold in the frequency-domain of acoustic signals. This method is used to solve the target recognition problem with two data sets to verify its effectiveness, after which the performance is analyzed. The result indicates that the manifold learning can discover the intrinsic feature and increase the accuracy and the robustness of low altitude passive acoustic target recognition system.
Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction
Zhou, Tianyi; Wu, Xindong
2010-01-01
It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \\cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local...
Nonlinear Bayesian cue integration explains the dynamics of vocal learning
Zhou, Baohua; Sober, Samuel; Nemenman, Ilya
The acoustics of vocal production in songbirds is tightly regulated during both development and adulthood as birds progressively refine their song using sensory feedback to match an acoustic target. Here, we perturb this sensory feedback using headphones to shift the pitch (fundamental frequency) of song. When the pitch is shifted upwards (downwards), birds eventually learn to compensate and sing lower (higher), bringing the experienced pitch closer to the target. Paradoxically, the speed and amplitude of this motor learning decrease with increases in the introduced error size, so that birds respond rapidly to a small sensory perturbation, while seemingly never correcting a much bigger one. Similar results are observed broadly across the animal kingdom, and they do not derive from a limited plasticity of the adult brain since birds can compensate for a large error as long as the error is imposed gradually. We develop a mathematical model based on nonlinear Bayesian integration of two sensory modalities (one perturbed and the other not) that quantitatively explains all of these observations. The model makes predictions about the structure of the probability distribution of the pitches sung by birds during the pitch shift experiments, which we confirm using experimental data. This work was supported in part by James S. McDonnell Foundation Grant # 220020321, NSF Grant # IOS/1208126, NSF Grant # IOS/1456912 and NIH Grants # R01NS084844.
Manifolds, sheaves, and cohomology
Wedhorn, Torsten
2016-01-01
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples. Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis Readership Graduate Students in Mathematics / Master of Science in Mathematics About the Author Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany.
The Identification of Convex Function on Riemannian Manifold
Directory of Open Access Journals (Sweden)
Li Zou
2014-01-01
Full Text Available The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.
Dimensionality reduction of collective motion by principal manifolds
Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.
2015-01-01
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.
Yamabe flow on Berwald manifolds
Azami, Shahroud; Razavi, Asadollah
2015-12-01
Studying the geometric flow plays a powerful role in mathematics and physics. We introduce the Yamabe flow on Finsler manifolds and we will prove the existence and uniqueness for solution of Yamabe flow on Berwald manifolds.
Hetero-manifold Regularisation for Cross-modal Hashing.
Zheng, Feng; Tang, Yi; Shao, Ling
2016-12-28
Recently, cross-modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi-modal data. To address both challenges, in this paper, we propose a novel method termed hetero-manifold regularisation (HMR) to supervise the learning of hash functions for efficient cross-modal search. A hetero-manifold integrates multiple sub-manifolds defined by homogeneous data with the help of cross-modal supervision information. Taking advantages of the hetero-manifold, the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero-manifold. Furthermore, a novel cumulative distance inequality defined on the hetero-manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes. By using the inequality, cross-modal hashing is transformed into a problem of hetero-manifold regularised support vector learning. Therefore, the performance of cross-modal search can be significantly improved by seamlessly combining the integrated information of the hetero-manifold and the strong generalisation of the support vector machine. Comprehensive experiments show that the proposed HMR achieve advantageous results over the state-of-the-art methods in several challenging cross-modal tasks.
Institute of Scientific and Technical Information of China (English)
宋涛; 汤宝平; 李锋
2013-01-01
针对旋转机械故障诊断需人工干预、精度低、故障样本难以获取等问题,提出基于流形学习和K-最近邻分类器(KNNC)的故障诊断模型.提取振动信号多域信息熵以全面反映设备运行状态并构造高维特征集；利用正交邻域保持嵌入(ONPE)非线性流形学习算法的二次特征提取特性进行维数约简使特征具有更好的聚类特性；基于改进的更适用于小样本分类KNNC进行模式识别,用轴承故障诊断案例证明该模型的有效性.%Considering the disadvantages existing in conventional fault diagnosis methods for rotating machinery, such as necessity of manual intervention, low accuracy and difficulty to obtain fault samples, a fault diagnosis method was proposed based on manifold learning and K-nearest neighbor classifier ( KNNC). Multi-domain information entropy of vibration signal was extracted to reflect fully the working status and construct high-dimensional characteristic sets. Then the second feature extraction property of the nonlinear manifold learning algorithm, orthogonal neighborhood preserving embedding( ONPE) , was used for dimensionality reduction and to make the features get better clustering property. Finally, improved KNNC was used for pattern classification. The method is more suitable for small sample classification. A diagnostic case of a bearing proves the effectiveness of the model.
Gómez, Gerard; Barrabés Vera, Esther
2011-01-01
The term Space Manifold Dynamics (SMD) has been proposed for encompassing the various applications of Dynamical Systems methods to spacecraft mission analysis and design, ranging from the exploitation of libration orbits around the collinear Lagrangian points to the design of optimal station-keeping and eclipse avoidance manoeuvres or the determination of low energy lunar and interplanetary transfers
Adaptive Neighborhood Selection Based on Local Linearity for Manifold Learning%流形学习中基于局部线性结构的自适应邻域选择
Institute of Scientific and Technical Information of China (English)
詹宇斌; 殷建平; 刘新旺; 张国敏
2011-01-01
Recently, manifold learning has attracted extensive interests of researchers from machine learning, pattern recognition, computer vision and related communities. Constructing a reasonable neighborhood for each point is a key issue in manifold learning. Conventional neighborhood selection algorithms k nearest neighbors (k-NN) and ε-neighborhood need to specifiy the parameter manually beforehand which most manifold learning algorithms are sensitive to. In this paper, an adaptive neighborhood selection algorithm based on local linearity called ANSLL is presented. Firstly, two principles of construction neighborhood for most existing manifold learning algorithms are summarized as: 1) data points in the same neighborhood should approximately lie on a d-dimensional linear subspace (d is the dimensionality of data manifold) and 2) each neighborhood should be as large as possible. Then based on these two principles, ANSLL exploits principal component analysis (PCA) technique to measure the linearity of finite data points set and constructs neighborhood for each point via neighborhood contraction or expansion. In addition, an improved method of constructing neighborhood graph, which can improve the accuracy of geodesic distance estimation for isometric embedding, is also proposed. Finally, extensive and systematic experiments on both synthetic data sets and real world data sets demonstrate that the ANSLL algorithm can adaptively tune neighborhood size according to local curvature of data manifold and then improve the performance of most existing manifold algorithms, such as Isomap and LLE.%近年来,流形学习成为包括机器学习、模式识别和计算机视觉等相关领域的研究热点.流形学习算法中,邻域选择直接关系到算法的性能,而传统的邻域选择算法如k近邻和ε邻域算法存在参数难以确定,所构建邻域不能反映流形学习算法对邻域要求等缺点.提出了一种基于流形局部线性结构的自适应邻
Eigenvalue pinching on spinc manifolds
Roos, Saskia
2017-02-01
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
Manifold Insulation for Solar Collectors
1982-01-01
Results of computer analysis of effects of various manifold insulation detailed in 23-page report show that if fluid is distributed to and gathered from array of solar collectors by external rather than internal manifold, effectiveness of manifold insulation has major influence on efficiency. Report describes required input data and presents equations that govern computer model. Provides graphs comparing collector efficiencies for representative manifold sizes and insulations.
Institute of Scientific and Technical Information of China (English)
张文林; 牛铜; 屈丹; 李弼程; 裴喜龙
2015-01-01
从语音信号声学特征空间的非线性流形结构特点出发,利用流形上的压缩感知原理,构建新的语音识别声学模型.将特征空间划分为多个局部区域,对每个局部区域用一个低维的因子分析模型进行近似,从而得到混合因子分析模型.将上下文相关状态的观测矢量限定在该非线性低维流形结构上,推导得到其观测概率模型.最终,每个状态由一个服从稀疏约束的权重矢量和若干个服从标准正态分布的低维局部因子矢量所决定.文中给出了局部区域潜在维数的确定准则及模型参数的迭代估计算法.基于RM 语料库的连续语音识别实验表明,相比于传统的高斯混合模型(Gaussian mixture model, GMM)和子空间高斯混合模型(Subspace Gaussian mixture model, SGMM),新声学模型在测试集上的平均词错误率(Word error rate, WER)分别相对下降了33.1%和9.2%.%Based on nonlinear manifold structure of acoustic feature space of speech signal, a new type of acoustic model for speech recognition is developed using compressive sensing. The feature space is divided into multiple local areas, with each area approximated by a low dimensional factor analysis model, so that in a mixture of factor analyzers is obtained. By restricting the observation vectors to be located on that nonlinear manifold, the probabilistic model of each context dependent state can be derived. Each state is determined by a sparse weight vector and several low-dimensional factors which follow standard Gaussian distributions. The principle for selection of the dimension for each local area is given, and iterated estimation methods for various model parameters are presented. Continuous speech recognition experiments on the RM corpus show that compared with the conventional Gaussian mixture model (GMM) and the subspace Gaussian mixture model (SGMM), the new acoustic model reduces the word error rate (WER) by 33.1%and 9.2%respectively.
Pulse Distributing Manifold; Pulse Distributing Manifold
Energy Technology Data Exchange (ETDEWEB)
Schutting, Eberhard [Technische Univ. Graz (Austria); Sams, Theodor [AVL List GmbH, Graz (Austria); Glensvig, Michael [Forschungsgesellschaft mbH, Graz (AT). Kompetenzzentrum ' ' Das virtuelle Fahrzeug' ' (VIF)
2011-07-01
The Pulse Distributing Manifold is a new charge exchange method for turbocharged diesel engines with exhaust gas recirculation (EGR). The method is characterized in that the EGR mass flow is not diverted from the exhaust gas mass flow continuously, but over time broken into sub-streams. The temporal interruption is achieved by two phase-shifted outlet valves which are connected via separate manifolds only with the turbocharger or only with the EGR path. The time points of valve opening are chosen such that the turbocharger and the aftertreatment process of exhaust gas is perfused by high-energy exhaust gas of the blowdown phase while cooler and less energy-rich exhaust gas of the exhaust period is used for the exhaust gas recirculation. This increases the enthalpy for the turbocharger and the temperature for the exhaust gas treatment, while the cooling efficiency at the EGR cooler is reduced. The elimination of the continuous EGR valve has a positive effect on pumping losses. The principle functioning and the potential of this system could be demonstrated by means of a concept study using one-dimensional simulations. Without disadvantages in fuel consumption for the considered commercial vehicle engine, a reduction the EGR cooler performance by 15 % and an increase in exhaust temperature of 35 K could be achieved. The presented charge exchange method was developed, evaluated and patented within the scope of the research program 'K2-mobility' of the project partners AVL (Mainz, Federal Republic of Germany) and University of Technology Graz (Austria). The research project 'K2-Mobility' is supported by the competence center 'The virtual vehicle' Forschungsgesellschaft mbH (Graz, Austria).
Characterizing humans on Riemannian manifolds.
Tosato, Diego; Spera, Mauro; Cristani, Marco; Murino, Vittorio
2013-08-01
In surveillance applications, head and body orientation of people is of primary importance for assessing many behavioral traits. Unfortunately, in this context people are often encoded by a few, noisy pixels so that their characterization is difficult. We face this issue, proposing a computational framework which is based on an expressive descriptor, the covariance of features. Covariances have been employed for pedestrian detection purposes, actually a binary classification problem on Riemannian manifolds. In this paper, we show how to extend to the multiclassification case, presenting a novel descriptor, named weighted array of covariances, especially suited for dealing with tiny image representations. The extension requires a novel differential geometry approach in which covariances are projected on a unique tangent space where standard machine learning techniques can be applied. In particular, we adopt the Campbell-Baker-Hausdorff expansion as a means to approximate on the tangent space the genuine (geodesic) distances on the manifold in a very efficient way. We test our methodology on multiple benchmark datasets, and also propose new testing sets, getting convincing results in all the cases.
Nonlinear Alignment and Its Local Linear Iterative Solution
Directory of Open Access Journals (Sweden)
Sumin Zhang
2016-01-01
Full Text Available In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…
Local Linear Regression on Manifolds and its Geometric Interpretation
Cheng, Ming-Yen
2012-01-01
We study nonparametric regression with high-dimensional data, when the predictors lie on an unknown, lower-dimensional manifold. In this context, recently \\cite{aswani_bickel:2011} suggested performing the conventional local linear regression (LLR) in the ambient space and regularizing the estimation problem using information obtained from learning the manifold locally. By contrast, our approach is to reduce the dimensionality first and then construct the LLR directly on a tangent plane approximation to the manifold. Under mild conditions, asymptotic expressions for the conditional mean squared error of the proposed estimator are derived for both the interior and the boundary cases. One implication of these results is that the optimal convergence rate depends only on the intrinsic dimension $d$ of the manifold, but not on the ambient space dimension $p$. Another implication is that the estimator is design adaptive and automatically adapts to the boundary of the unknown manifold. The bias and variance expressi...
Akbulut, Selman
2010-01-01
It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. Using this property, we give simple constructions of various cork structures of 4-manifolds. We also give an example of infinitely many disjoint embeddings of a fixed cork into a non-compact 4-manifold which produce infinitely many exotic smooth structures (recall that [7] gives examples arbitrarily many disjoint imbeddings of different corks in a closed manifold inducing mutually different exotic structures). Furthermore, here we construct arbitrary many simply connected compact codimention zero submanifolds of S^4 which are mutually homeomorphic but not diffeomorphic.
Canonical metrics on complex manifold
Institute of Scientific and Technical Information of China (English)
YAU Shing-Tung
2008-01-01
@@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Canonical metrics on complex manifold
Institute of Scientific and Technical Information of China (English)
YAU; Shing-Tung(Yau; S.-T.)
2008-01-01
Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.
Probabilistic Universal Learning Networks and their Applications to Nonlinear Control Systems
1998-01-01
Probabilistic Universal Learning Networks (PrULNs) are proposed, which are learning networks with a capability of dealing with stochastic signals. PrULNs are extensions of Universal Learning Networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. A generalized learning algorithm has been devised for ULNs which can also be used in a unified manner for almost all kinds of learn...
Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.
Sun, Shiliang; Xie, Xijiong
2016-09-01
Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.
Aytuna, Aydin
2011-01-01
An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among them. In section 3 we relate some of these notions to the linear topological type of the Fr\\'echet space of analytic functions on the given manifold. In sections 4 and 5 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.
Learning from experience in nonlinear environments: Evidence from a competition scenario.
Soyer, Emre; Hogarth, Robin M
2015-09-01
We test people's ability to learn to estimate a criterion (probability of success in a competition scenario) that requires aggregating information in a nonlinear manner. The learning environments faced by experimental participants are kind in that they are characterized by immediate, accurate feedback involving either naturalistic outcomes (information on winning and/or ranking) or the normatively correct probabilities. We find no evidence of learning from the former and modest learning from the latter, except that a group of participants endowed with a memory aid performed substantially better. However, when the task is restructured such that information should be aggregated in a linear fashion, participants learn to make more accurate assessments. Our experiments highlight the important role played by prior beliefs in learning tasks, the default status of linear aggregation in many inferential judgments, and the difficulty of learning in nonlinear environments even in the presence of veridical feedback. Copyright © 2015 Elsevier Inc. All rights reserved.
Orthogonal Sparsity Preserving Discriminant Analysis Based on Manifold Learning%基于流形学习的正交稀疏保留投影鉴别分析
Institute of Scientific and Technical Information of China (English)
凌若冰; 荆晓远; 吴飞; 姚永芳; 李文倩
2015-01-01
Sparsity Preserving Projections ( SPP) is an effective feature extraction method,which can preserve the sparse reconstruction re-lations among samples. However,according to the manifold learning theory,the local manifold structure of samples is more important than the global Euclidean structure of samples. SPP cannot get a set of orthogonal projection vectors,and thus there exists redundant informa-tion among the obtained features. To address these problems of SPP,propose a novel approach called Manifold Learning based Iterative Orthogonal Sparsity preserving Discriminant Analysis ( MLIOSDA) ,which introduces the idea of manifold learning into SPP and obtains orthogonal projection space. Obtain optimal projection vectors in an iterative manner. Also provide a terminating criterion to finish the it-eration. Experimental results on CAS-PEAL and PolyU databases demonstrate that the proposed approach can effectively improve the rec-ognition results compared with some related methods.%稀疏保留投影( SPP)是一种保留样本间的稀疏重构关系的特征提取方法。但是根据流形学习理论,考虑局部流形结构比考虑全局欧氏结构更重要。此外,SPP得到的不是一组正交的投影向量,特征间存在冗余信息。为解决该问题,文中提出一种改进的稀疏保留投影算法,在SPP中引入有监督的流形学习,使得所得投影空间正交,并用迭代的方式求解最优投影变换,称为基于流形学习的迭代正交稀疏保留鉴别分析( MLIOSDA)。同时提出一种终止准则终止迭代。在CAS-PEAL人脸数据库和PolyU掌纹数据库的实验结果表明,文中提出的方法与一些相关方法相比有效地提高了识别结果。
基于流形学习的视频中文文本检测算法%Automatic Chinese Text Detection in Video Frames Based on Manifold Learning
Institute of Scientific and Technical Information of China (English)
王文震
2012-01-01
Put forward based on the manifold learning video Chinese text detection algorithm is proposed. Algorithm for image and text on the text image feature extraction, manifold dimension reduction, classifier training, and other key parts were improved, and for the collection of text image with the sample text sample image feature extraction, and use mapping manifold learning algorithm is introduced to complete the characteristic dimension reduction, finally using support vector machine classifier to complete the training, get the text with the text detection classifier, complete video Chinese text detection. The experimental results show that the new algorithm has obvious advantages in the test reliability and precision are improved greatly, and has a certain practical significance.%提出了一种基于流形学习的视频中文文本检测算法.算法重点针对文本图像和非文本图像的特征提取、流形降维、分类器训练等关键部分进行了改进,对人为收集的文本图像样本与非文本图像样本进行特征提取,并使用等距离映射的流形学习算法来完成特征降维,最后使用支持向量机来完成分类器训练,获取文本与非文本检测分类器,完成视频中文文本检测.实验结果表明,算法具有明显优越性,在检测可靠性和准确度上有较大提高,具有一定的实用意义.
Institute of Scientific and Technical Information of China (English)
马婧华; 汤宝平; 宋涛
2015-01-01
Aiming at the problem that the actual engineering vibration signals are interfered by strong noise with strong nonlinear characteristic,a phase space reconstruction method based on adaptive intrinsic dimension estimation manifold learning was proposed.Firstly,one-dimensional time series containing noise were reconstructed into a high dimensional phase space with the phase space reconstruction method.Secondly,the intrinsic dimension of each sample point in the phase space was estimated based on the maximum likelihood estimate (MLE),the adaptive weighted average method was used to calculate the global intrinsic dimension.At last,the manifold learning algorithm and the local tangent space alignment (LTSA)were employed to project the signal containing noise from the high-dimensional phase space into the intrinsic dimensional space of useful signals.After eliminating the noise distributing in the high-dimensional space, the signals were reconstructed back into one-dimensional time series.Lorenz simulation and an example of vibration signals'noise reduction for a wind power generator unit showed that the proposed method has a good performance of nonlinear noise reduction.%针对实际工程领域振动信号噪声干扰大、具有强烈非线性等问题，提出了基于自适应本征维数估计流形学习的相空间重构降噪方法。利用相空间重构将一维含噪时间序列重构到高维相空间；基于极大似然估计法（maximum likelihood estimate，MLE）估计相空间中每个样本点的本征维数并使用自适应加权平均法计算全局本征维数；采用局部切空间排列（Local tangent space Alignment，LTSA）流形学习方法将含噪信号从高维相空间投影到有用信号的本征维空间中，剔除分布在高维空间中的噪声后，重构回一维时间序列。通过 Lorenz 仿真实验和风电机组振动信号降噪实例，证实了该方法具有良好的非线性降噪性能。
First-order D-type Iterative Learning Control for Nonlinear Systems with Unknown Relative Degree
Institute of Scientific and Technical Information of China (English)
SONGZhao-Qing; MAOJian-Qin; DAIShao-Wu
2005-01-01
The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.
Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation
Weigang Wen; Gao, Robert X.; Weidong Cheng
2016-01-01
The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by w...
Holonomy groups of Lorentzian manifolds
Galaev, Anton S
2016-01-01
In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker metrics and the classification of 2-symmetric Lorentzian manifolds are considered.
Quantum manifolds with classical limit
Hohmann, Manuel; Wohlfarth, Mattias N R
2008-01-01
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the manifold structure of spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity.
Analysis, manifolds and physics
Choquet-Bruhat, Y
2000-01-01
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.
Daverman, Robert J
2007-01-01
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve
A Multi-manifold Learning Algorithm Based on Locally Linear Embedding%一种基于局部线性嵌入的多流形学习算法
Institute of Scientific and Technical Information of China (English)
李燕燕; 闫德勤; 刘胜蓝; 郑宏亮
2012-01-01
In order to improve the correctness of locally linear embedding caused by multi-manifold data, a novel multi-manifold learning algorithm based on locally linear embedding is proposed in this paper. It accords the cam distribution to find neighbors of data points, and avoid the lack of the direction of neighbor selection; and a positive regularization is added in the gaining of the optimal reconstruction weight matrix to make it insensitive to the noise. Located in different manifolds for the high-dimensional data on the experiment to test the improved algorithm has a good effort of reducing dimension. Image retrieval using the COIL-20 database show that the improved algorithm has the practical value in the multi-class and multi-shape manifold learning.%针对局部线性嵌入算法在处理多流形数据时失效问题,提出一种新的基于局部线性嵌入的多流形学习算法.采用cam分布寻找数据点的近邻,避免了近邻选取方向的缺失；同时在获取重建权值矩阵的过程中引入一个正则项约束,从而降低了算法对噪声的敏感度.通过对分布在不同流形上的高维数据实验后发现改进算法具有很好的降维效果.为了进一步验证算法的有效性,将改进后的算法对COIL-20数据库进行图像检索,结果表明该算法不仅有较好的降维效果而且在多类别多形状流形学习中有很好的实用价值.
Sequential Nonlinear Learning for Distributed Multiagent Systems via Extreme Learning Machines.
Vanli, Nuri Denizcan; Sayin, Muhammed O; Delibalta, Ibrahim; Kozat, Suleyman Serdar
2017-03-01
We study online nonlinear learning over distributed multiagent systems, where each agent employs a single hidden layer feedforward neural network (SLFN) structure to sequentially minimize arbitrary loss functions. In particular, each agent trains its own SLFN using only the data that is revealed to itself. On the other hand, the aim of the multiagent system is to train the SLFN at each agent as well as the optimal centralized batch SLFN that has access to all the data, by exchanging information between neighboring agents. We address this problem by introducing a distributed subgradient-based extreme learning machine algorithm. The proposed algorithm provides guaranteed upper bounds on the performance of the SLFN at each agent and shows that each of these individual SLFNs asymptotically achieves the performance of the optimal centralized batch SLFN. Our performance guarantees explicitly distinguish the effects of data- and network-dependent parameters on the convergence rate of the proposed algorithm. The experimental results illustrate that the proposed algorithm achieves the oracle performance significantly faster than the state-of-the-art methods in the machine learning and signal processing literature. Hence, the proposed method is highly appealing for the applications involving big data.
Institute of Scientific and Technical Information of China (English)
宋涛; 汤宝平; 邓蕾
2014-01-01
针对现有的批量式流形学习算法无法利用已学习的流形结构实现新增样本的快速约简的缺点，提出增殖正交邻域保持嵌入（Incremental Orthogonal Neighborhood Preserving Embedding，IONPE）流形学习算法。该算法在正交邻域保持嵌入算法基础上利用分块处理思想实现新增样本子集的动态约简。从原始样本中选取部分重叠点合并至新增样本，对重叠点和新增样本子集不依赖原始样本使用正交邻域保持嵌入（ONPE）进行独立约简获取低维嵌入坐标子集，并基于重叠点坐标差值最小化原则，将新增样本低维嵌入坐标通过旋转平移缩放整合到原样本子集中。齿轮箱故障诊断案例证实了IONPE算法具有良好的增量学习能力，在继承ONPE优良聚类特性的同时有效提高了新增样本约简效率。%The current batch manifold learning algorithms can't achieve rapid dimension reduction of additional samples with learned manifold structures.Here,the incremental orthogonal neighborhood preserving embedding (IONPE) manifold learning algorithm was proposed.With it,dynamic incremental learning for additional samples was realized with a block processing idea based on orthogonal neighborhood preserving embedding.Firstly,some overlapping points were selected from the original samples and added to the additional samples. Secondly, the subset of low-dimensional embedding coordinates of additional samples was obtained with ONPE independing on the original samples.Finally,based on the principle of minimizing the differences of the overlapping point coordinates,the low-dimensional embedding coordinates of the additional samples were integrated into the original samples with rotating, shifting and scaling transformations.The fault diagnosis case of a gearbox confirmed that the IONPE algorithm has a good incremental learning ability,it improves the processing efficiency of the additional samples while inheriting the
Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds
Barreto, Yadira; Verjovsky, Alberto
2013-01-01
We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.
The Koppelman-Leray formula on complex Finsler manifolds
Institute of Scientific and Technical Information of China (English)
QIU Chunhui; ZHONG Tongde
2005-01-01
By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.
Vibration control of a nonlinear quarter-car active suspension system by reinforcement learning
Bucak, İ. Ö.; Öz, H. R.
2012-06-01
This article presents the investigation of performance of a nonlinear quarter-car active suspension system with a stochastic real-valued reinforcement learning control strategy. As an example, a model of a quarter car with a nonlinear suspension spring subjected to excitation from a road profile is considered. The excitation is realised by the roughness of the road. The quarter-car model to be considered here can be approximately described as a nonlinear two degrees of freedom system. The experimental results indicate that the proposed active suspension system suppresses the vibrations greatly. A simulation of a nonlinear quarter-car active suspension system is presented to demonstrate the effectiveness and examine the performance of the learning control algorithm.
Online identification of nonlinear spatiotemporal systems using kernel learning approach.
Ning, Hanwen; Jing, Xingjian; Cheng, Li
2011-09-01
The identification of nonlinear spatiotemporal systems is of significance to engineering practice, since it can always provide useful insight into the underlying nonlinear mechanism and physical characteristics under study. In this paper, nonlinear spatiotemporal system models are transformed into a class of multi-input-multi-output (MIMO) partially linear systems (PLSs), and an effective online identification algorithm is therefore proposed by using a pruning error minimization principle and least square support vector machines. It is shown that many benchmark physical and engineering systems can be transformed into MIMO-PLSs which keep some important physical spatiotemporal relationships and are very helpful in the identification and analysis of the underlying system. Compared with several existing methods, the advantages of the proposed method are that it can make full use of some prior structural information about system physical models, can realize online estimation of the system dynamics, and achieve accurate characterization of some important nonlinear physical characteristics of the system. This would provide an important basis for state estimation, control, optimal analysis, and design of nonlinear distributed parameter systems. The proposed algorithm can also be applied to identification problems of stochastic spatiotemporal dynamical systems. Numeral examples and comparisons are given to demonstrate our results.
Local Schrodinger flow into Kahler manifolds
Institute of Scientific and Technical Information of China (English)
DlNG; Weiyue(
2001-01-01
［1］Ding, W. Y. , Wang, Y. D. , Schrodinger flows of maps into symplectic manifolds, Science in China, Ser. A, 1998, 41(7): 746.［2］Landau, L. D., Lifshitz, E. M., On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Z.Sowj., 1935, 8: 153; reproduced in Collected Papers of L. D. Landau, New York: Pergaman Press, 1965, 101－114.［3］Faddeev, L., Takhtajan, L. A. , Hamiltonian Methods in the Theory of Solitons, Berlin-Heidelberg-New York: Springer-Verlag, 1987.［4］Nakamura, K., Sasada, T., Soliton and wave trains in ferromagnets, Phys. Lett. A, 1974, 48: 321.［5］Zhou, Y. , Guo, B. , Tan, S. , Existence and uniqueness of smooth solution for system of ferromagnetic chain, Science in China, Ser. A, 1991, 34(3): 257.［6］Pang, P. , Wang, H. , Wang, Y. D. , Schrodinger flow of maps into Kahler manifolds, Asian J. of Math. , in press.［7］Wang, H. , Wang, Y. D. , Global inhomogeneous Schrodinger flow, Int. J. Math., 2000, 11: 1079.［8］Pang, P., Wang, H., Wang, Y. D., Local existence for inhomogeneous Schrodinger flow of maps into Kahler manifolds,Acta Math. Sinica, English Series, 2000, 16: 487.［9］Temg, C. L., Uhlenbeck, K., Schrodinger flows on Grassmannians, in Integrable Systems, Geometry and Topology,Somervi11e, MA: International Press, in press.［10］Chang, N., Shatah, J., Uhlenbeck, K., Schrodinger maps, Commun. Pure Appl. Math., 2000, 53: 157.［11］Wang, Y. D., Ferromagnetic chain equation from a closed Riemannian manifold into S2, Int. J. Math., 1995, 6: 93.［12］Wang, Y. D., Heisenberg chain systems from compact manifolds into S2, J. Math. Phys., 1998, 39(1): 363.［13］Sulem, P., Sulem, C., Bardos, C., On the continuous limit for a system of classical spins, Commun. Math. Phys., 1986,107: 431.［14］Aubin, T., Nonlinear Analysis on Manifolds, Monge-Ampère Equations, Berlin-Heidelberg-New York: Springer-Verlag,1982.［15］Eells, J. , Lemaire, L. , Another report on harmonic maps, Bull. London
LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
Wei GAO; Zheng TIAN
2009-01-01
An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.
Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays
Institute of Scientific and Technical Information of China (English)
Wei-Sheng Chen; Rui-Hong Li; Jing Li
2010-01-01
An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.
Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process
Directory of Open Access Journals (Sweden)
Dazi Li
2015-01-01
Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.
Park, Hyunjin
2012-04-04
Neuroimaging data are high dimensional and thus cumbersome to analyze. Manifold learning is a technique to find a low dimensional representation for high dimensional data. With manifold learning, data analysis becomes more tractable in the low dimensional space. We propose a novel shape quantification method based on a manifold learning method, ISOMAP, for brain MRI. Existing work applied another manifold learning method, multidimensional scaling (MDS), to quantify shape information for distinguishing Alzheimer's disease (AD) from normal. We enhance the existing methodology by (1) applying it to distinguish mild cognitive impairment (MCI) from normal, (2) adopting a more advanced manifold learning technique, ISOMAP, and (3) showing the effectiveness of the induced low dimensional embedding space to predict key clinical variables such as mini mental state exam scores and clinical diagnosis using the standard multiple linear regression. Our methodology was tested using 25 normal, 25 AD, and 25 MCI patients.
Quasi-Newton Exploration of Implicitly Constrained Manifolds
Tang, Chengcheng
2011-08-01
A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.
Manifold statistics for essential matrices
Dubbelman, G.; Dorst, L.; Pijls, H.; Fitzgibbon, A.; et al.,
2012-01-01
Riemannian geometry allows for the generalization of statistics designed for Euclidean vector spaces to Riemannian manifolds. It has recently gained popularity within computer vision as many relevant parameter spaces have such a Riemannian manifold structure. Approaches which exploit this have been
Lu, Zhao; Sun, Jing; Butts, Kenneth
2016-02-03
A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.
Ouali, D.; Chebana, F.; Ouarda, T. B. M. J.
2017-06-01
The high complexity of hydrological systems has long been recognized. Despite the increasing number of statistical techniques that aim to estimate hydrological quantiles at ungauged sites, few approaches were designed to account for the possible nonlinear connections between hydrological variables and catchments characteristics. Recently, a number of nonlinear machine-learning tools have received attention in regional frequency analysis (RFA) applications especially for estimation purposes. In this paper, the aim is to study nonlinearity-related aspects in the RFA of hydrological variables using statistical and machine-learning approaches. To this end, a variety of combinations of linear and nonlinear approaches are considered in the main RFA steps (delineation and estimation). Artificial neural networks (ANNs) and generalized additive models (GAMs) are combined to a nonlinear ANN-based canonical correlation analysis (NLCCA) procedure to ensure an appropriate nonlinear modeling of the complex processes involved. A comparison is carried out between classical linear combinations (CCAs combined with linear regression (LR) model), semilinear combinations (e.g., NLCCA with LR) and fully nonlinear combinations (e.g., NLCCA with GAM). The considered models are applied to three different data sets located in North America. Results indicate that fully nonlinear models (in both RFA steps) are the most appropriate since they provide best performances and a more realistic description of the physical processes involved, even though they are relatively more complex than linear ones. On the other hand, semilinear models which consider nonlinearity either in the delineation or estimation steps showed little improvement over linear models. The linear approaches provided the lowest performances.
基于通勤时间距离的流形聚类与可视化%Manifold Clustering and Visualization with Commute Time Distance
Institute of Scientific and Technical Information of China (English)
邵超; 张啸剑
2015-01-01
T he existing manifold learning algorithms can effectively learn and visualize the low‐dimensional nonlinear manifold structure of high‐dimensional data . However ,most efforts to date select the neighborhood size in sensitivity and difficulty ,and require sampling the data from a single manifold .To reduce the sensitivity of manifold learning algorithms to the neighborhood size ,and address the effective visualization and clustering of multi‐manifold data , this paper employs the commute time distance to propose a novel manifold learning algorithm , called CTD‐ISOMAP (commute time distance isometric mapping ) . Compared with Euclidean distance , commute time distance probabilistically synthesizes all the paths connecting any two points in the neighborhood graph .Consequently ,it takes into account the intrinsic nonlinear geometric structure for the given data ,w hile still providing the robust results ,and then is suitable to identify the shortcut edges and the inter‐manifold edges possibly existed in the neighborhood graph .CTD‐ISOMAP with the commute time distance ,therefore ,effectively eliminates the shortcut edges in the neighborhood graph ,so that each output achieves the low‐dimensional nonlinear manifold structure in the much wider range of the neighborhood size ,and eliminates the inter‐manifold edges in the neighborhood graph to boost the clustering on multi‐manifold data obtained by spectral clustering .Finally ,our experimental study verifies the effectiveness of CTD‐ISOMAP .%现有流形学习算法能比较好地学习和可视化高维数据的低维非线性流形结构，但对难以高效选取的邻域大小参数还比较敏感，且要求数据良好采样于单一流形。为了降低流形学习算法对邻域大小参数的敏感程度，并实现对多流形数据的良好聚类与可视化，提出了1种新的基于通勤时间距离的流形学习算法———CTD‐ISOMAP（commute time distance isometric mapping
Inverse Learning Control of Nonlinear Systems Using Support Vector Machines
Institute of Scientific and Technical Information of China (English)
HU Zhong-hui; LI Yuan-gui; CAI Yun-ze; XU Xiao-ming
2005-01-01
An inverse learning control scheme using the support vector machine (SVM) for regression was proposed. The inverse learning approach is originally researched in the neural networks. Compared with neural networks, SVMs overcome the problems of local minimum and curse of dimensionality. Additionally, the good generalization performance of SVMs increases the robustness of control system. The method of designing SVM inverselearning controller was presented. The proposed method is demonstrated on tracking problems and the performance is satisfactory.
PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System
Institute of Scientific and Technical Information of China (English)
LUO Xiaohui; ZHU Yuquan; HU Junhua
2009-01-01
For the electro-hydraulic servo vibrating system(ESVS) with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control(ILC), is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time's tracking error of the system and then applies the error information to the next time's control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro-hydraulic servo vibrating system.
Cohomotopy sets of 4-manifolds
Kirby, Robion; Teichner, Peter
2012-01-01
Elementary geometric arguments are used to compute the group of homotopy classes of maps from a 4-manifold X to the 3-sphere, and to enumerate the homotopy classes of maps from X to the 2-sphere. The former completes a project initiated by Steenrod in the 1940's, and the latter provides geometric arguments for and extensions of recent homotopy theoretic results of Larry Taylor. These two results complete the computation of all the cohomotopy sets of closed oriented 4-manifolds and provide a framework for the study of Morse 2-functions on 4-manifolds, a subject that has garnered considerable recent attention.
Teaching and Learning the Interplay between Chance and Determinism in Nonlinear Systems
Stavrou, Dimitrios; Duit, Reinders
2014-01-01
That the interplay of random and deterministic processes may result in both the limited predictability of nonlinear systems and the formation of structures seems to be a most valuable general insight into the nature of science. This study investigates the possibility of teaching and learning the interplay of chance and determinism in nonlinear…
Lee, Miriam Chang Yi; Chow, Jia Yi; Komar, John; Tan, Clara Wee Keat; Button, Chris
2014-01-01
Learning a sports skill is a complex process in which practitioners are challenged to cater for individual differences. The main purpose of this study was to explore the effectiveness of a Nonlinear Pedagogy approach for learning a sports skill. Twenty-four 10-year-old females participated in a 4-week intervention involving either a Nonlinear Pedagogy (i.e.,manipulation of task constraints including equipment and rules) or a Linear Pedagogy (i.e., prescriptive, repetitive drills) approach to learn a tennis forehand stroke. Performance accuracy scores, movement criterion scores and kinematic data were measured during pre-intervention, post-intervention and retention tests. While both groups showed improvements in performance accuracy scores over time, the Nonlinear Pedagogy group displayed a greater number of movement clusters at post-test indicating the presence of degeneracy (i.e., many ways to achieve the same outcome). The results suggest that degeneracy is effective for learning a sports skill facilitated by a Nonlinear Pedagogy approach. These findings challenge the common misconception that there must be only one ideal movement solution for a task and thus have implications for coaches and educators when designing instructions for skill acquisition.
Institute of Scientific and Technical Information of China (English)
付冬暇; 赵淮; 李爱霞
2013-01-01
提出了一种基于流形学习的航空影像匹配方法.该方法利用同一幅影像中特征点之间的空间结构和不同影像中特征点之间的相似性作为特征点映射的约束条件,利用流形学习方法对影像的特征点进行映射,将所有影像的特征点映射到同一空间后采用最小距离方法进行特征点的匹配.利用实际的航空影像进行实验,与SIFT方法、SVD-LLE方法进行综合分析,结果表明本文方法在匹配性能方面具有明显的优越性,并且能够同时获得多幅影像之间的匹配关系.%This paper proposes a matching method about aerial images of surveying based on manifold learning.Based on manifold learning,and by using the differencies of spatial structures among feature points in one image and similarities among feature points in different images,this method mapping all feature points in a same space,then matching them in min distance classification.By using actual aerial images of surveying,comprehensive analysis and SIFT method,SVD-LLE method,the results of experiment show that this method not only has obvious advantages in matching performance,but also can obtain the matching relationship between multiple images.
Haantjes Manifolds and Integrable Systems
Tempesta, Piergiulio
2014-01-01
A general theory of integrable systems is proposed, based on the theory of Haantjes manifolds. We introduce the notion of symplectic-Haantjes manifold (or $\\omega \\mathcal{H}$ manifold), as the natural setting where the notion of integrability can be formulated. We propose an approach to the separation of variables for classical systems, related to the geometry of Haantjes manifolds. A special class of coordinates, called Darboux-Haantjes coordinates, will be constructed from the Haantjes structure associated with an integrable systems. They enable the additive separation of variables of the Hamilton-Jacobi equation. We also present an application of our approach to the study of some finite-dimensional integrable models, as the H\\'enon-Heiles systems and a stationary reduction of the KdV hierarchy.
An introduction to differential manifolds
Lafontaine, Jacques
2015-01-01
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...
Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes
DEFF Research Database (Denmark)
Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo
2012-01-01
In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...
Lu, Zhao; Sun, Jing; Butts, Kenneth
2014-05-01
Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.
Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems.
Dai, Shi-Lu; Wang, Cong; Wang, Min
2014-01-01
This paper studies the problem of learning from adaptive neural network (NN) control of a class of nonaffine nonlinear systems in uncertain dynamic environments. In the control design process, a stable adaptive NN tracking control design technique is proposed for the nonaffine nonlinear systems with a mild assumption by combining a filtered tracking error with the implicit function theorem, input-to-state stability, and the small-gain theorem. The proposed stable control design technique not only overcomes the difficulty in controlling nonaffine nonlinear systems but also relaxes constraint conditions of the considered systems. In the learning process, the partial persistent excitation (PE) condition of radial basis function NNs is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition and an appropriate state transformation, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the implicit desired control input dynamics in the stable control process and of storing the learned knowledge in memory. Subsequently, an NN learning control design technique that effectively exploits the learned knowledge without re-adapting to the controller parameters is proposed to achieve closed-loop stability and improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
Invariant Manifolds and Collective Coordinates
Papenbrock, T
2001-01-01
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.
Discriminative Nonlinear Analysis Operator Learning: When Cosparse Model Meets Image Classification
Wen, Zaidao; Hou, Biao; Jiao, Licheng
2017-07-01
Linear synthesis model based dictionary learning framework has achieved remarkable performances in image classification in the last decade. Behaved as a generative feature model, it however suffers from some intrinsic deficiencies. In this paper, we propose a novel parametric nonlinear analysis cosparse model (NACM) with which a unique feature vector will be much more efficiently extracted. Additionally, we derive a deep insight to demonstrate that NACM is capable of simultaneously learning the task adapted feature transformation and regularization to encode our preferences, domain prior knowledge and task oriented supervised information into the features. The proposed NACM is devoted to the classification task as a discriminative feature model and yield a novel discriminative nonlinear analysis operator learning framework (DNAOL). The theoretical analysis and experimental performances clearly demonstrate that DNAOL will not only achieve the better or at least competitive classification accuracies than the state-of-the-art algorithms but it can also dramatically reduce the time complexities in both training and testing phases.
Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation
Directory of Open Access Journals (Sweden)
Weigang Wen
2016-01-01
Full Text Available The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by wavelet enveloping. The envelope energy is adopted as an indicator to select meshing frequency band. Manifold learning is utilized to reduce the effect of noise within meshing frequency band. The fault characteristic frequency of the planetary gear is shown by spectrogram. The planetary gearbox model and test rig are established and experiments with planet gear faults are conducted for verification. All results of experiment analysis demonstrate its effectiveness and reliability.
Hyperbolic normal forms and invariant manifolds: Astronomical applications
Directory of Open Access Journals (Sweden)
Efthymiopoulos C.
2012-01-01
Full Text Available In recent years, the study of the dynamics induced by the invariant manifolds of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has led to a number of applications in celestial mechanics and dynamical astronomy. Two applications of main current interest are i space manifold dynamics, i.e. the use of the manifolds in space mission design, and, in a quite different context, ii the study of spiral structure in galaxies. At present, most approaches to the computation of orbits associated with manifold dynamics (i.e. periodic or asymptotic orbits rely either on the use of the so-called Poincaré - Lindstedt method, or on purely numerical methods. In the present article we briefly review an analytic method of computation of invariant manifolds, first introduced by Moser (1958, and developed in the canonical framework by Giorgilli (2001. We use a simple example to demonstrate how hyperbolic normal form computations can be performed, and we refer to the analytic continuation method of Ozorio de Almeida and co-workers, by which we can considerably extend the initial domain of convergence of Moser’s normal form.
Visual words assignment via information-theoretic manifold embedding.
Deng, Yue; Li, Yipeng; Qian, Yanjun; Ji, Xiangyang; Dai, Qionghai
2014-10-01
Codebook-based learning provides a flexible way to extract the contents of an image in a data-driven manner for visual recognition. One central task in such frameworks is codeword assignment, which allocates local image descriptors to the most similar codewords in the dictionary to generate histogram for categorization. Nevertheless, existing assignment approaches, e.g., nearest neighbors strategy (hard assignment) and Gaussian similarity (soft assignment), suffer from two problems: 1) too strong Euclidean assumption and 2) neglecting the label information of the local descriptors. To address the aforementioned two challenges, we propose a graph assignment method with maximal mutual information (GAMI) regularization. GAMI takes the power of manifold structure to better reveal the relationship of massive number of local features by nonlinear graph metric. Meanwhile, the mutual information of descriptor-label pairs is ultimately optimized in the embedding space for the sake of enhancing the discriminant property of the selected codewords. According to such objective, two optimization models, i.e., inexact-GAMI and exact-GAMI, are respectively proposed in this paper. The inexact model can be efficiently solved with a closed-from solution. The stricter exact-GAMI nonparametrically estimates the entropy of descriptor-label pairs in the embedding space and thus leads to a relatively complicated but still trackable optimization. The effectiveness of GAMI models are verified on both the public and our own datasets.
Enhanced manifold regularization for semi-supervised classification.
Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong
2016-06-01
Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.
Zhang, Ruikun; Hou, Zhongsheng; Ji, Honghai; Yin, Chenkun
2016-04-01
In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov-Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Learning and Adaptive Hybrid Systems for Nonlinear Control
1991-05-01
6 2.1.1 Single Layer Networks 8 Perceptrons 8 Samuel’s Checker Player 10 ADALINE and MADALINE 12 2.1.2 Multilayer Networks 13 Hebbian Learning 13...was Widrow’s ADALINE and MADALINE [Wid89]. He developed a type of adaptive filter which is still in widespread use today in such items as high speed...time step, and used it for pattern recognition. This "Adaptive Linear Neuron" ( ADALINE ) [Wid89] was then built in actual hardware, where weights were
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
Qi, Peng; Hu, Xiaolin
2014-04-01
It is well known that there exist nonlinear statistical regularities in natural images. Existing approaches for capturing such regularities always model the image intensities by assuming a parameterized distribution for the intensities and learn the parameters. In the letter, we propose to model the outer product of image intensities by assuming a gaussian distribution for it. A two-layer structure is presented, where the first layer is nonlinear and the second layer is linear. Trained on natural images, the first-layer bases resemble the receptive fields of simple cells in the primary visual cortex (V1), while the second-layer units exhibit some properties of the complex cells in V1, including phase invariance and masking effect. The model can be seen as an approximation of the covariance model proposed in Karklin and Lewicki (2009) but has more robust and efficient learning algorithms.
Unobstructedness of deformations of holomorphic maps onto Fano manifolds of Picard number 1
Hwang, Jun-Muk
2009-01-01
We show that deformations of a surjective morphism onto a Fano manifold of Picard number 1 are unobstructed and rigid modulo the automorphisms of the target, if the variety of minimal rational tangents of the Fano manifold is non-linear or finite. The condition on the variety of minimal rational tangents holds for practically all known examples of Fano manifolds of Picard number 1, except the projective space. When the variety of minimal rational tangents is non-linear, the proof is based on an earlier result of N. Mok and the author on the birationality of the tangent map. When the varieties of minimal rational tangents of the Fano manifold is finite, the key idea is to factorize the given surjective morphism, after some transformation, through a universal morphism associated to the minimal rational curves.
Epileptic EEG classification based on extreme learning machine and nonlinear features.
Yuan, Qi; Zhou, Weidong; Li, Shufang; Cai, Dongmei
2011-09-01
The automatic detection and classification of epileptic EEG are significant in the evaluation of patients with epilepsy. This paper presents a new EEG classification approach based on the extreme learning machine (ELM) and nonlinear dynamical features. The theory of nonlinear dynamics has been a powerful tool for understanding brain electrical activities. Nonlinear features extracted from EEG signals such as approximate entropy (ApEn), Hurst exponent and scaling exponent obtained with detrended fluctuation analysis (DFA) are employed to characterize interictal and ictal EEGs. The statistics indicate that the differences of those nonlinear features between interictal and ictal EEGs are statistically significant. The ELM algorithm is employed to train a single hidden layer feedforward neural network (SLFN) with EEG nonlinear features. The experiments demonstrate that compared with the backpropagation (BP) algorithm and support vector machine (SVM), the performance of the ELM is better in terms of training time and classification accuracy which achieves a satisfying recognition accuracy of 96.5% for interictal and ictal EEG signals. Copyright © 2011 Elsevier B.V. All rights reserved.
The use of machine learning and nonlinear statistical tools for ADME prediction.
Sakiyama, Yojiro
2009-02-01
Absorption, distribution, metabolism and excretion (ADME)-related failure of drug candidates is a major issue for the pharmaceutical industry today. Prediction of ADME by in silico tools has now become an inevitable paradigm to reduce cost and enhance efficiency in pharmaceutical research. Recently, machine learning as well as nonlinear statistical tools has been widely applied to predict routine ADME end points. To achieve accurate and reliable predictions, it would be a prerequisite to understand the concepts, mechanisms and limitations of these tools. Here, we have devised a small synthetic nonlinear data set to help understand the mechanism of machine learning by 2D-visualisation. We applied six new machine learning methods to four different data sets. The methods include Naive Bayes classifier, classification and regression tree, random forest, Gaussian process, support vector machine and k nearest neighbour. The results demonstrated that ensemble learning and kernel machine displayed greater accuracy of prediction than classical methods irrespective of the data set size. The importance of interaction with the engineering field is also addressed. The results described here provide insights into the mechanism of machine learning, which will enable appropriate usage in the future.
Fivebranes and 3-manifold homology
Gukov, Sergei; Vafa, Cumrun
2016-01-01
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only...... in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimize a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend...... from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls...
Lattice QCD on nonorientable manifolds
Mages, Simon; Tóth, Bálint C.; Borsányi, Szabolcs; Fodor, Zoltán; Katz, Sándor D.; Szabó, Kálmán K.
2017-05-01
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a nonorientable manifold and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is that translational invariance is preserved up to exponentially small corrections. A Dirac fermion on a nonorientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.
Parallel spinors on flat manifolds
Sadowski, Michał
2006-05-01
Let p(M) be the dimension of the vector space of parallel spinors on a closed spin manifold M. We prove that every finite group G is the holonomy group of a closed flat spin manifold M(G) such that p(M(G))>0. If the holonomy group Hol(M) of M is cyclic, then we give an explicit formula for p(M) another than that given in [R.J. Miatello, R.A. Podesta, The spectrum of twisted Dirac operators on compact flat manifolds, Trans. Am. Math. Soc., in press]. We answer the question when p(M)>0 if Hol(M) is a cyclic group of prime order or dimM≤4.
Motion Planning via Manifold Samples
Salzman, Oren; Raveh, Barak; Halperin, Dan
2011-01-01
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generi...
Fivebranes and 3-manifold homology
Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun
2017-07-01
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[ M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.
Institute of Scientific and Technical Information of China (English)
赵立杰; 王海龙; 陈斌
2016-01-01
The wastewater treatment process is vulnerable to the impact of external shocks to cause sludge floating, aging, poisoning, expansion and other failure conditions, resulting in effluent deterioration and high energy consumption. It is urgent to quickly and accurately identify the operating conditions of wastewater treatment process. In the existing supervised learning methods all the data are labeled which are time consuming and expensive. A multitude of unlabeled data to collect easily and cheaply have rich and useful information about the operating condition. To overcome the disadvantage of supervised learning algorithms that they cannot make use of unlabeled data, a semi-supervised extreme learning machine algorithm based on manifold regularization is adopted to monitor the operation states of biochemical wastewater treatment process. The graph Laplacian matrix is constructed from both the labeled patterns and the unlabeled patterns. Extreme learning machine algorithm is adopted to handle the semi-supervised learning task under the framework of the manifold regularization. It constructs the hidden layer using random feature mapping and solves the weights between the hidden layer and the output layer, which exhibit the computational efficiency and generalization performance of the random neural network. The results of simulation experiments show that the fault identification method based on semi supervised learning machine has superiority to the basic extreme learning machine in improving the accuracy and reliability.%污水处理过程容易受外界冲激扰动影响，引发污泥上浮、老化、中毒、膨胀等故障工况，导致出水水质质量差，能源消耗高等问题，如何快速准确识别污水操作工况故障至关重要。针对污水工况识别过程中现有监督学习方法未利用大量未标记数据蕴含的丰富操作工况信息，采用基于流形正则化极限学习机的半监督学习方法，监视生化污水处
Geometric Schr(o)dinger-Airy Flows on K(a)hler Manifolds
Institute of Scientific and Technical Information of China (English)
Xiao Wei SUN; You De WANG
2013-01-01
We define a class of geometric flows on a complete K(a)hler manifold to unify some physical and mechanical models such as the motion equations of vortex filament,complex-valued mKdV equations,derivative nonlinear Schr(o)dinger equations etc.Furthermore,we consider the existence for these flows from S1 into a complete K(a)hler manifold and prove some local and global existence results.
Invariant manifolds and collective coordinates
Energy Technology Data Exchange (ETDEWEB)
Papenbrock, T. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Institute for Nuclear Theory, University of Washington, Seattle, WA (United States); Seligman, T.H. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Centro de Ciencias Fisicas, University of Mexico (UNAM), Cuernavaca (Mexico)
2001-09-14
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction. (author)
Stein Manifolds and Holomorphic Mappings
Forstneric, Franc
2011-01-01
The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. This book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applicat
Multiscale singular value manifold for rotating machinery fault diagnosis
Energy Technology Data Exchange (ETDEWEB)
Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)
2017-01-15
Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.
Behavior of Graph Laplacians on Manifolds with Boundary
Zhou, Xueyuan
2011-01-01
In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from sampled data to certain continuous operators has become an active research topic recently. Most of the existing work has been done under the assumption that the data is sampled from a manifold without boundary or that the functions of interests are evaluated at a point away from the boundary. However, the question of boundary behavior is of considerable practical and theoretical interest. In this paper we provide an analysis of the behavior of graph Laplacians at a point near or on the boundary, discuss their convergence rates and their implications and provide some numerical results. It turns out that while points near the boundary occupy only a small part of the total volume of a manifold, the behavior of graph Laplacian there has different scaling properties from its beh...
Mitigating noise in global manifold coordinates for hyperspectral image classification
Jin, Can; Bachmann, Charles M.
2016-09-01
Over the past decade, manifold and graph representations of hyperspectral imagery (HSI) have been explored widely in HSI applications. Among many data-driven approaches to deriving manifold coordinate representations including Isometric Mapping (ISOMAP), Local Linear Embedding (LLE), Laplacian Eigenmaps (LE), and Diffusion Kernels (DK), ISOMAP is the only global method that well represents the large scale nonlinear geometric structure of the data. In recent years, methods such as ENH-ISOMAP as well as its parallel computing accelerations makes ISOMAP practical for hyperspectral image dimensionality reduction. However, the noise problem in these methods has not been well addressed, which is critical to classification accuracy based on the manifold coordinates derived from these methods. While standard linear techniques to reduce the effects of noise can be applied as a preliminary step, these are based on global statistics and are applied globally across the entire data set, resulting in the risk of losing subtle nonlinear features before classification. To solve this problem, in this paper, we explore several approaches to modeling and mitigating noise in HSI in a local sense to improve the performance of the ENH-ISOMAP algorithm, aiming to reduce the noise effect on the manifold representations of the HSI. A new method to split data into local spectral subsets is introduced. Based on the local spectral subsets obtained with this method, a local noise model guided landmark selection scheme is proposed. In addition, a new robust adaptive neighborhood method using intrinsic dimensionality information to construct the k-Nearest Neighbor graph is introduced to increase the fidelity of the graph, based on the same framework of local spectral subsetting. The improved algorithm produces manifold coordinates with less noise, and shows a better classification accuracy using k-Nearest Neighbor classifier.
Variable selection in identification of a high dimensional nonlinear non-parametric system
Institute of Scientific and Technical Information of China (English)
Er-Wei BAI; Wenxiao ZHAO; Weixing ZHENG
2015-01-01
The problem of variable selection in system identification of a high dimensional nonlinear non-parametric system is described. The inherent difficulty, the curse of dimensionality, is introduced. Then its connections to various topics and research areas are briefly discussed, including order determination, pattern recognition, data mining, machine learning, statistical regression and manifold embedding. Finally, some results of variable selection in system identification in the recent literature are presented.
Boski, Marcin; Paszke, Wojciech
2017-01-01
This paper deals with designing of iterative learning control schemes for uncertain systems with static nonlinearities. More specifically, the nonlinear part is supposed to be sector bounded and system matrices are assumed to range in the polytope of matrices. For systems with such nonlinearities and uncertainties the repetitive process setting is exploited to develop a linear matrix inequality based conditions for computing the feedback and feedforward (learning) controllers. These controllers guarantee acceptable dynamics along the trials and ensure convergence of the trial-to-trial error dynamics, respectively. Numerical examples illustrate the theoretical results and confirm effectiveness of the designed control scheme.
Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2015-05-01
This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.
Layered models for closed 3-manifolds
Johnson, Jesse
2010-01-01
We define a combinatorial structure on 3-manifolds that combines the model manifolds constructed in Minsky's proof of the ending lamination conjecture with the layered triangulations defined by Jaco and Rubinstein.
Holomorphic flexibility properties of complex manifolds
2004-01-01
We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic manifolds.
Periodic solutions and slow manifolds
Verhulst, F.
2006-01-01
After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we disc
Melnikov Vector and Heteroclinic Manifolds
Institute of Scientific and Technical Information of China (English)
朱德明
1994-01-01
Using the exponential dichotomies,the transversality theory and the generalized Melnikov method,we consider the conditions for the persistence and the transversality of the singular orbit,with high degeneracy,situated on the heteroclinic or homoclinic manifold under perturbation.The results obtained extend,include and improve the corresponding ones given in certain papers well known in this area.
Cobordism Independence of Grassmann Manifolds
Indian Academy of Sciences (India)
Ashish Kumar Das
2004-02-01
This note proves that, for $F=\\mathbb{R},\\mathbb{C}$ or $\\mathbb{H}$, the bordism classes of all non-bounding Grassmannian manifolds $G_k(F^{n+k})$, with < and having real dimension , constitute a linearly independent set in the unoriented bordism group $\\mathfrak{N}_d$ regarded as a $\\mathbb{Z}_2$-vector space.
Fluid delivery manifolds and microfluidic systems
Energy Technology Data Exchange (ETDEWEB)
Renzi, Ronald F.; Sommer, Gregory J.; Singh, Anup K.; Hatch, Anson V.; Claudnic, Mark R.; Wang, Ying-Chih; Van de Vreugde, James L.
2017-02-28
Embodiments of fluid distribution manifolds, cartridges, and microfluidic systems are described herein. Fluid distribution manifolds may include an insert member and a manifold base and may define a substantially closed channel within the manifold when the insert member is press-fit into the base. Cartridges described herein may allow for simultaneous electrical and fluidic interconnection with an electrical multiplex board and may be held in place using magnetic attraction.
Quantization of Presymplectic Manifolds and Circle Actions
Silva, A C; Tolman, S; Silva, Ana Canas da; Karshon, Yael; Tolman, Susan
1997-01-01
We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
Invariant manifolds for flows in Banach Spaces
Energy Technology Data Exchange (ETDEWEB)
Lu Kening.
1989-01-01
The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.
Local Schrodinger flow into Kahler manifolds
Institute of Scientific and Technical Information of China (English)
丁伟岳; 王友德
2001-01-01
In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.
HOLOMORPHIC MANIFOLDS ON LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
Tsoy-Wo Ma
2005-01-01
Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.
On the manifold-mapping optimization technique
Echeverria, D.; Hemker, P.W.
2006-01-01
In this paper, we study in some detail the manifold-mapping optimization technique introduced in an earlier paper. Manifold mapping aims at accelerating optimal design procedures that otherwise require many evaluations of time-expensive cost functions. We give a proof of convergence for the manifold
Directory of Open Access Journals (Sweden)
George P. Papaioannou
2016-08-01
Full Text Available In this work we propose a new hybrid model, a combination of the manifold learning Principal Components (PC technique and the traditional multiple regression (PC-regression, for short and medium-term forecasting of daily, aggregated, day-ahead, electricity system-wide load in the Greek Electricity Market for the period 2004–2014. PC-regression is shown to effectively capture the intraday, intraweek and annual patterns of load. We compare our model with a number of classical statistical approaches (Holt-Winters exponential smoothing of its generalizations Error-Trend-Seasonal, ETS models, the Seasonal Autoregressive Moving Average with exogenous variables, Seasonal Autoregressive Integrated Moving Average with eXogenous (SARIMAX model as well as with the more sophisticated artificial intelligence models, Artificial Neural Networks (ANN and Support Vector Machines (SVM. Using a number of criteria for measuring the quality of the generated in-and out-of-sample forecasts, we have concluded that the forecasts of our hybrid model outperforms the ones generated by the other model, with the SARMAX model being the next best performing approach, giving comparable results. Our approach contributes to studies aimed at providing more accurate and reliable load forecasting, prerequisites for an efficient management of modern power systems.
Smolders, K.; Volckaert, M.; Swevers, J.
2008-11-01
This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.
Infinite horizon self-learning optimal control of nonaffine discrete-time nonlinear systems.
Wei, Qinglai; Liu, Derong; Yang, Xiong
2015-04-01
In this paper, a novel iterative adaptive dynamic programming (ADP)-based infinite horizon self-learning optimal control algorithm, called generalized policy iteration algorithm, is developed for nonaffine discrete-time (DT) nonlinear systems. Generalized policy iteration algorithm is a general idea of interacting policy and value iteration algorithms of ADP. The developed generalized policy iteration algorithm permits an arbitrary positive semidefinite function to initialize the algorithm, where two iteration indices are used for policy improvement and policy evaluation, respectively. It is the first time that the convergence, admissibility, and optimality properties of the generalized policy iteration algorithm for DT nonlinear systems are analyzed. Neural networks are used to implement the developed algorithm. Finally, numerical examples are presented to illustrate the performance of the developed algorithm.
Yang, Xiong; Liu, Derong; Wang, Ding
2014-03-01
In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.
Person-Independent Head Pose Estimation Using Biased Manifold Embedding
Directory of Open Access Journals (Sweden)
Sethuraman Panchanathan
2008-02-01
Full Text Available Head pose estimation has been an integral problem in the study of face recognition systems and human-computer interfaces, as part of biometric applications. A fine estimate of the head pose angle is necessary and useful for several face analysis applications. To determine the head pose, face images with varying pose angles can be considered to be lying on a smooth low-dimensional manifold in high-dimensional image feature space. However, when there are face images of multiple individuals with varying pose angles, manifold learning techniques often do not give accurate results. In this work, we propose a framework for a supervised form of manifold learning called Biased Manifold Embedding to obtain improved performance in head pose angle estimation. This framework goes beyond pose estimation, and can be applied to all regression applications. This framework, although formulated for a regression scenario, unifies other supervised approaches to manifold learning that have been proposed so far. Detailed studies of the proposed method are carried out on the FacePix database, which contains 181 face images each of 30 individuals with pose angle variations at a granularity of 1Ã¢ÂˆÂ˜. Since biometric applications in the real world may not contain this level of granularity in training data, an analysis of the methodology is performed on sparsely sampled data to validate its effectiveness. We obtained up to 2Ã¢ÂˆÂ˜ average pose angle estimation error in the results from our experiments, which matched the best results obtained for head pose estimation using related approaches.
Zhang, Xian-Xia; Jiang, Ye; Li, Han-Xiong; Li, Shao-Yuan
2013-10-01
A data-driven 3-D fuzzy-logic controller (3-D FLC) design methodology based on support vector regression (SVR) learning is developed for nonlinear spatially distributed dynamic systems. Initially, the spatial information expression and processing as well as the fuzzy linguistic expression and rule inference of a 3-D FLC are integrated into spatial fuzzy basis functions (SFBFs), and then the 3-D FLC can be depicted by a three-layer network structure. By relating SFBFs of the 3-D FLC directly to spatial kernel functions of an SVR, an equivalence relationship of the 3-D FLC and the SVR is established, which means that the 3-D FLC can be designed with the help of the SVR learning. Subsequently, for an easy implementation, a systematic SVR learning-based 3-D FLC design scheme is formulated. In addition, the universal approximation capability of the proposed 3-D FLC is presented. Finally, the control of a nonlinear catalytic packed-bed reactor is considered as an application to demonstrate the effectiveness of the proposed 3-D FLC.
Singular reduction of generalized complex manifolds
Goldberg, Timothy E
2010-01-01
In this paper, we develop the analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for reduction of Hamiltonian generalized Kaehler manifolds.
Yang, Xiong; Liu, Derong; Wang, Ding; Wei, Qinglai
2014-07-01
In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input-multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov's direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach.
Stochastic gradient descent on Riemannian manifolds
Bonnabel, Silvere
2011-01-01
Stochastic gradient descent is a simple appproach to find the local minima of a function whose evaluations are corrupted by noise. In this paper, mostly motivated by machine learning applications, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and we show several well-known algorithms can be cast in our versatile geometric framework. We also address the gain tuning issue in connection with the tools of the recent theory of symmetry-preserving observers.
Manifold seal structure for fuel cell stack
Collins, William P.
1988-01-01
The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.
PD-type iterative learning control for nonlinear time-delay system with external disturbance
Institute of Scientific and Technical Information of China (English)
Zhang Baolin; Tang Gongyou; Zheng Shi
2006-01-01
The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.
Tawel, Raoul (Inventor)
1994-01-01
A method for the rapid learning of nonlinear mappings and topological transformations using a dynamically reconfigurable artificial neural network is presented. This fully-recurrent Adaptive Neuron Model (ANM) network was applied to the highly degenerate inverse kinematics problem in robotics, and its performance evaluation is bench-marked. Once trained, the resulting neuromorphic architecture was implemented in custom analog neural network hardware and the parameters capturing the functional transformation downloaded onto the system. This neuroprocessor, capable of 10(exp 9) ops/sec, was interfaced directly to a three degree of freedom Heathkit robotic manipulator. Calculation of the hardware feed-forward pass for this mapping was benchmarked at approximately 10 microsec.
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... theorems together with the comparison techniques for distance functions in Riemannian geometry and obtain bounds for the first Dirichlet eigenvalues, the exit times and the capacities as well as isoperimetric type inequalities for so-called extrinsic $R-$webs of minimal webs in ambient Riemannian manifolds...
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Rigid subsets of symplectic manifolds
Entov, Michael
2007-01-01
We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the previous work of P.Albers) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.
Torsions of 3-dimensional manifolds
Wurzbacher, T
2002-01-01
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews
Koppelman formulas on flag manifolds
Samuelsson, Håkan
2010-01-01
We construct Koppelman formulas on manifolds of flags in $\\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $\\debar$-equation. We also construct reproducing kernels for harmonic $(p,q)$-forms in the case of Grassmannians.
Polynomial Regression on Riemannian Manifolds
Hinkle, Jacob; Fletcher, P Thomas; Joshi, Sarang
2012-01-01
In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.
Deformations of extremal toric manifolds
Rollin, Yann
2012-01-01
Let $X$ be a compact toric extremal K\\"ahler manifold. Using the work of Sz\\'ekelyhidi, we provide a simple criterion on the fan describing $X$ to ensure the existence of complex deformations of $X$ that carry extremal metrics. As an example, we find new CSC metrics on 4-points blow-ups of $\\C\\P^1\\times\\C\\P^1$.
The Operator Manifold Formalism, 1
Ter-Kazarian, G T
1998-01-01
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the spacetime continuum and internal worlds, where the subquarks are defined implying the Confinement and Gauge principles. This formalism in Part II (hep-th/9812182) is used to develop further the microscopic approach to some key problems of particle physics.
Coincidence classes in nonorientable manifolds
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We study Nielsen coincidence theory for maps between manifolds of same dimension regardless of orientation. We use the definition of semi-index of a class, review the definition of defective classes, and study the occurrence of defective root classes. We prove a semi-index product formula for lifting maps and give conditions for the defective coincidence classes to be the only essential classes.
Manifolds of interconvertible pure states
Sinolecka, Magdalena M.; Zyczkowski, Karol; Kus, Marek
2001-01-01
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.
Manifolds of interconvertible pure states
Sinolecka, M M; Kus, M; Sinolecka, Magdalena M.; Zyczkowski, Karol; Kus, Marek
2002-01-01
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.
On Einstein, Hermitian 4-Manifolds
LeBrun, Claude
2010-01-01
Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # (-CP2), or the Einstein metric on CP2 # 2 (-CP2) constructed in Chen-LeBrun-Weber.
Suliman, Suha Ibrahim
Landsat 7 Enhanced Thematic Mapper Plus (ETM+) Scan Line Corrector (SLC) device, which corrects for the satellite motion, has failed since May 2003 resulting in a loss of about 22% of the data. To improve the reconstruction of Landsat 7 SLC-off images, Locally Linear Manifold (LLM) model is proposed for filling gaps in hyperspectral imagery. In this approach, each spectral band is modeled as a non-linear locally affine manifold that can be learned from the matching bands at different time instances. Moreover, each band is divided into small overlapping spatial patches. In particular, each patch is considered to be a linear combination (approximately on an affine space) of a set of corresponding patches from the same location that are adjacent in time or from the same season of the year. Fill patches are selected from Landsat 5 Thematic Mapper (TM) products of the year 1984 through 2011 which have similar spatial and radiometric resolution as Landsat 7 products. Using this approach, the gap-filling process involves feasible point on the learned manifold to approximate the missing pixels. The proposed LLM framework is compared to some existing single-source (Average and Inverse Distance Weight (IDW)) and multi- source (Local Linear Histogram Matching (LLHM) and Adaptive Window Linear Histogram Matching (AWLHM)) gap-filling methodologies. We analyze the effectiveness of the proposed LLM approach through simulation examples with known ground-truth. It is shown that the LLM-model driven approach outperforms all existing recovery methods considered in this study. The superiority of LLM is illustrated by providing better reconstructed images with higher accuracy even over heterogeneous landscape. Moreover, it is relatively simple to realize algorithmically, and it needs much less computing time when compared to the state- of-the art AWLHM approach.
Model Reduction by Manifold Boundaries
Transtrum, Mark K.; Qiu, Peng
2015-01-01
Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce “black boxes” disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees of freedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically “compressed” into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions. PMID:25216014
Reservoir computing and extreme learning machines for non-linear time-series data analysis.
Butcher, J B; Verstraeten, D; Schrauwen, B; Day, C R; Haycock, P W
2013-02-01
Random projection architectures such as Echo state networks (ESNs) and Extreme Learning Machines (ELMs) use a network containing a randomly connected hidden layer and train only the output weights, overcoming the problems associated with the complex and computationally demanding training algorithms traditionally used to train neural networks, particularly recurrent neural networks. In this study an ESN is shown to contain an antagonistic trade-off between the amount of non-linear mapping and short-term memory it can exhibit when applied to time-series data which are highly non-linear. To overcome this trade-off a new architecture, Reservoir with Random Static Projections (R(2)SP) is investigated, that is shown to offer a significant improvement in performance. A similar approach using an ELM whose input is presented through a time delay (TD-ELM) is shown to further enhance performance where it significantly outperformed the ESN and R(2)SP as well other architectures when applied to a novel task which allows the short-term memory and non-linearity to be varied. The hard-limiting memory of the TD-ELM appears to be best suited for the data investigated in this study, although ESN-based approaches may offer improved performance when processing data which require a longer fading memory.
$\\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
Aprile, Francesco
2016-01-01
General half-BPS A-type boundary conditions are formulated for N=2 supersymmetric field theories on compact 3-manifolds with boundary. We observe that under suitable conditions manifolds of the real A-type admitting two complex supersymmetries (related by charge conjugation) possess, besides a contact structure, a natural integrable toric foliation. A boundary, or a general co-dimension-1 defect, can be inserted along any leaf of this preferred foliation to produce manifolds with boundary that have the topology of a solid torus. We show that supersymmetric field theories on such manifolds can be endowed with half-BPS A-type boundary conditions. We specify the natural curved space generalization of the A-type projection of bulk supersymmetries and analyze the resulting A-type boundary conditions in generic 3d non-linear sigma models and YM/CS-matter theories.
Smooth Maps of a Foliated Manifold in a Symplectic Manifold
Indian Academy of Sciences (India)
Mahuya Datta; Md Rabiul Islam
2009-06-01
Let be a smooth manifold with a regular foliation $\\mathcal{F}$ and a 2-form which induces closed forms on the leaves of $\\mathcal{F}$ in the leaf topology. A smooth map $f:(M,\\mathcal{F})\\longrightarrow(N, )$ in a symplectic manifold $(N, )$ is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the restriction of $f^∗$ is the same as the restriction of on each leaf of the foliation. If is a foliated symplectic immersion then the derivative map $Df$ gives rise to a bundle morphism $F:TM\\longrightarrow TN$ which restricts to a monomorphism on $T\\mathcal{F}\\subseteq TM$ and satisfies the condition $F^∗=$ on $T\\mathcal{F}$. A natural question is whether the existence of such a bundle map ensures the existence of a foliated symplectic immersion . As we shall see in this paper, the obstruction to the existence of such an is only topological in nature. The result is proved using the ℎ-principle theory of Gromov.
Differential Calculus on N-Graded Manifolds
Sardanashvily, G.; W. Wachowski
2017-01-01
The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a s...
Discrete equations and the singular manifold method
Estévez, P G
1999-01-01
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.
OBJECTORIENTED NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The design and management of the objects about the numerical manifold method are studied by abstracting the finite cover system of numerical manifold method as independent data classes and the theoretical basis for the researching and expanding of numerical manifold method is also put forward. The Hammer integration of triangular area coordinates is used in the integration of the element. The calculation result shows that the program is accuracy and effective.
Homology group on manifolds and their foldings
Directory of Open Access Journals (Sweden)
M. Abu-Saleem
2010-03-01
Full Text Available In this paper, we introduce the definition of the induced unfolding on the homology group. Some types of conditional foldings restricted on the elements of the homology groups are deduced. The effect of retraction on the homology group of a manifold is dicussed. The unfolding of variation curvature of manifolds on their homology group are represented. The relations between homology group of the manifold and its folding are deduced.
Hidden torsion, 3-manifolds, and homology cobordism
Cha, Jae Choon
2011-01-01
This paper continues our exploration of homology cobordism of 3-manifolds using our recent results on Cheeger-Gromov rho-invariants associated to amenable representations. We introduce a new type of torsion in 3-manifold groups we call hidden torsion, and an algebraic approximation we call local hidden torsion. We construct infinitely many hyperbolic 3-manifolds which have local hidden torsion in the transfinite lower central subgroup. By realizing Cheeger-Gromov invariants over amenable groups, we show that our hyperbolic 3-manifolds are not pairwise homology cobordant, yet remain indistinguishable by any prior known homology cobordism invariants.
Pro jective vector fields on Finsler manifolds
Institute of Scientific and Technical Information of China (English)
TIAN Huang-jia
2014-01-01
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.
Stability of Strongly Gauduchon Manifolds under Modifications
Popovici, Dan
2010-01-01
In our previous works on deformation limits of projective and Moishezon manifolds, we introduced and made crucial use of the notion of strongly Gauduchon metrics as a reinforcement of the earlier notion of Gauduchon metrics. Using direct and inverse images of closed positive currents of type $(1, \\, 1)$ and regularisation, we now show that compact complex manifolds carrying strongly Gauduchon metrics are stable under modifications. This stability property, known to fail for compact K\\"ahler manifolds, mirrors the modification stability of balanced manifolds proved by Alessandrini and Bassanelli.
The Fibered Isomorphism Conjecture for Complex Manifolds
Institute of Scientific and Technical Information of China (English)
S. K. ROUSHON
2007-01-01
In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones,corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.
Spectral gaps, inertial manifolds and kinematic dynamos
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es
2005-10-17
Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Integral formulas for differential forms of type(p,q)on complex Finsler manifolds
Institute of Scientific and Technical Information of China (English)
QIU; Chunhui; ZHONG; Tongde
2004-01-01
Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut,complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theory on complex Finsler manifolds. The Koppelman and Koppelman-Leray formulas are obtained, and the (θ)-equations are solved.
Holographic dimensional reduction: Center manifold theorem and E-infinity
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, University of Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)
2006-08-15
Klein modular curve is shown to be the holographic boundary of E-infinity Cantorian spacetime. The conformal relation between the full dimensional and the reduced space is explored. We show that both spaces analyzed in the appropriate manner give the same results for certain aspects of high energy particle physics and quantum gravity. Similarity with the center manifold theorem of non-linear dynamics and the theory of bifurcating vector fields is discussed. In particular it was found that the transfinite version of the E{sub 8}-bar E{sub 8} theory corresponds to a fuzzy Kahler manifold with b{sub 2}{sup -}=19-{phi}{sup 6} and b{sub 2}{sup +}=5+{phi}{sup 3}, while the boundary theory of the {gamma}{sub c}(7) Klein modular space corresponds to another fuzzy Kahler manifold with b{sub 2}{sup -}=13-{phi}{sup 6} and b{sub 2}{sup +}=3-{phi}{sup 6}. Based on these results, we conclude that the {epsilon}{sup ({approx}}{sup )}-{gamma}{sub c}(7) theory represents a worked out example for the correctness of the holographic principle first proposed by G. 't Hooft. Hooft.
Networked iterative learning control approach for nonlinear systems with random communication delay
Liu, Jian; Ruan, Xiaoe
2016-12-01
This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.
Musical Instrument Classification Based on Nonlinear Recurrence Analysis and Supervised Learning
Directory of Open Access Journals (Sweden)
R.Rui
2013-04-01
Full Text Available In this paper, the phase space reconstruction of time series produced by different instruments is discussed based on the nonlinear dynamic theory. The dense ratio, a novel quantitative recurrence parameter, is proposed to describe the difference of wind instruments, stringed instruments and keyboard instruments in the phase space by analyzing the recursive property of every instrument. Furthermore, a novel supervised learning algorithm for automatic classification of individual musical instrument signals is addressed deriving from the idea of supervised non-negative matrix factorization (NMF algorithm. In our approach, the orthogonal basis matrix could be obtained without updating the matrix iteratively, which NMF is unable to do. The experimental results indicate that the accuracy of the proposed method is improved by 3% comparing with the conventional features in the individual instrument classification.
Liu, Yan-Jun; Li, Jing; Tong, Shaocheng; Chen, C L Philip
2016-07-01
In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.
Stylianou, Agni
2003-06-01
Digital texts which are based on hypertext and hypermedia technologies are now being used to support science learning. Hypertext offers certain opportunities for learning as well as difficulties that challenge readers to become metacognitively aware of their navigation decisions in order to trade both meaning and structure while reading. The goal of this study was to investigate whether supporting sixth grade students to monitor and regulate their navigation behavior while reading from hypertext would lead to better navigation and learning. Metanavigation support in the form of prompts was provided to groups of students who used a hypertext system called CoMPASS to complete a design challenge. The metanavigation prompts aimed at encouraging students to understand the affordances of the navigational aids in CoMPASS and use them to guide their navigation. The study was conducted in a real classroom setting during the implementation of CoMPASS in sixth grade science classes. Multiple sources of group and individual data were collected and analyzed. Measures included student's individual performance in a pre-science knowledge test, the Metacognitive Awareness of Reading Strategies Inventory (MARSI), a reading comprehension test and a concept map test. Process measures included log file information that captured group navigation paths during the use of CoMPASS. The results suggested that providing metanavigation support enabled the groups to make coherent transitions among the text units. Findings also revealed that reading comprehension, presence of metanavigation support and prior domain knowledge significantly predicted students' individual understanding of science. Implications for hypertext design and literacy research fields are discussed.
Localization using omnivision-based manifold particle filters
Wong, Adelia; Yousefhussien, Mohammed; Ptucha, Raymond
2015-01-01
Developing precise and low-cost spatial localization algorithms is an essential component for autonomous navigation systems. Data collection must be of sufficient detail to distinguish unique locations, yet coarse enough to enable real-time processing. Active proximity sensors such as sonar and rangefinders have been used for interior localization, but sonar sensors are generally coarse and rangefinders are generally expensive. Passive sensors such as video cameras are low cost and feature-rich, but suffer from high dimensions and excessive bandwidth. This paper presents a novel approach to indoor localization using a low cost video camera and spherical mirror. Omnidirectional captured images undergo normalization and unwarping to a canonical representation more suitable for processing. Training images along with indoor maps are fed into a semi-supervised linear extension of graph embedding manifold learning algorithm to learn a low dimensional surface which represents the interior of a building. The manifold surface descriptor is used as a semantic signature for particle filter localization. Test frames are conditioned, mapped to a low dimensional surface, and then localized via an adaptive particle filter algorithm. These particles are temporally filtered for the final localization estimate. The proposed method, termed omnivision-based manifold particle filters, reduces convergence lag and increases overall efficiency.
A spectral characterization of nonlinear normal modes
Cirillo, G. I.; Mauroy, A.; Renson, L.; Kerschen, G.; Sepulchre, R.
2016-09-01
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.
Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics
Yavari, Arash
2012-03-09
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.
Integrability conditions on Engel-type manifolds
Calin, Ovidiu; Chang, Der-Chen; Hu, Jishan
2015-09-01
We introduce the concept of Engel manifold, as a manifold that resembles locally the Engel group, and find the integrability conditions of the associated sub-elliptic system , . These are given by , . Then an explicit construction of the solution involving an integral representation is provided, which corresponds to a Poincaré-type lemma for the Engel's distribution.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
Li, Tao
2011-01-01
We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also construct toroidal such examples containing hyperbolic JSJ pieces.
Gauged supergravities from Bianchi's group manifolds
Bergshoeff, E; Gran, U; Linares, R; Nielsen, M; Ortin, T; Roest, D
2004-01-01
We construct maximal D = 8 gauged supergravities by the reduction of D = I I supergravity over three-dimensional group manifolds. Such manifolds are classified into two classes, A and B, and eleven types. This Bianchi classification carries over to the gauged supergravities. The class A theories hav
Simplicial approach to derived differential manifolds
Borisov, Dennis
2011-01-01
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings (D.Spivak), thus preserving the classical cobordism ring. This reduction to the usual algebraic homotopy can potentially lead to virtual fundamental classes beyond obstruction theory.
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
YOE ITOKAWA; KATSUHIRO SHIOHAMA; BANKTESHWAR TIWARI
2016-10-01
The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.
Manifold: a Custom Analytics Platform to Visualize Research Impact
Directory of Open Access Journals (Sweden)
Steven Braun
2015-10-01
Full Text Available The use of research impact metrics and analytics has become an integral component to many aspects of institutional assessment. Many platforms currently exist to provide such analytics, both proprietary and open source; however, the functionality of these systems may not always overlap to serve uniquely specific needs. In this paper, I describe a novel web-based platform, named Manifold, that I built to serve custom research impact assessment needs in the University of Minnesota Medical School. Built on a standard LAMP architecture, Manifold automatically pulls publication data for faculty from Scopus through APIs, calculates impact metrics through automated analytics, and dynamically generates report-like profiles that visualize those metrics. Work on this project has resulted in many lessons learned about challenges to sustainability and scalability in developing a system of such magnitude.
Time-frequency manifold sparse reconstruction: A novel method for bearing fault feature extraction
Ding, Xiaoxi; He, Qingbo
2016-12-01
In this paper, a novel transient signal reconstruction method, called time-frequency manifold (TFM) sparse reconstruction, is proposed for bearing fault feature extraction. This method introduces image sparse reconstruction into the TFM analysis framework. According to the excellent denoising performance of TFM, a more effective time-frequency (TF) dictionary can be learned from the TFM signature by image sparse decomposition based on orthogonal matching pursuit (OMP). Then, the TF distribution (TFD) of the raw signal in a reconstructed phase space would be re-expressed with the sum of learned TF atoms multiplied by corresponding coefficients. Finally, one-dimensional signal can be achieved again by the inverse process of TF analysis (TFA). Meanwhile, the amplitude information of the raw signal would be well reconstructed. The proposed technique combines the merits of the TFM in denoising and the atomic decomposition in image sparse reconstruction. Moreover, the combination makes it possible to express the nonlinear signal processing results explicitly in theory. The effectiveness of the proposed TFM sparse reconstruction method is verified by experimental analysis for bearing fault feature extraction.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, Jaap
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.
Warped product submanifolds of Lorentzian paracosymplectic manifolds
Perkta\\cs, Selcen Yüksel; Kele\\cs, Sad\\ik
2011-01-01
In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\\times_{f}M_{\\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ is an usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold.
Heterotic model building: 16 special manifolds
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford OX14JD (United Kingdom); Lee, Seung-Joo [School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of); Lukas, Andre; Sun, Chuang [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom)
2014-06-12
We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.
Heisenberg symmetry and hypermultiplet manifolds
Antoniadis, Ignatios; Petropoulos, P Marios; Siampos, Konstantinos
2015-01-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.
Heisenberg symmetry and hypermultiplet manifolds
Directory of Open Access Journals (Sweden)
Ignatios Antoniadis
2016-04-01
Full Text Available We study the emergence of Heisenberg (Bianchi II algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N=2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U(1×U(1 at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg⋉U(1. We finally discuss the realization of the latter by gauging appropriate Sp(2,4 generators in N=2 conformal supergravity.
Function theory on symplectic manifolds
Polterovich, Leonid
2014-01-01
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...
Harmonic space and quaternionic manifolds
Galperin, A; Ogievetsky, O V
1994-01-01
We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic ...
Improving the Critic Learning for Event-Based Nonlinear H∞ Control Design.
Wang, Ding; He, Haibo; Liu, Derong
2017-01-30
In this paper, we aim at improving the critic learning criterion to cope with the event-based nonlinear H∞ state feedback control design. First of all, the H∞ control problem is regarded as a two-player zero-sum game and the adaptive critic mechanism is used to achieve the minimax optimization under event-based environment. Then, based on an improved updating rule, the event-based optimal control law and the time-based worst-case disturbance law are obtained approximately by training a single critic neural network. The initial stabilizing control is no longer required during the implementation process of the new algorithm. Next, the closed-loop system is formulated as an impulsive model and its stability issue is handled by incorporating the improved learning criterion. The infamous Zeno behavior of the present event-based design is also avoided through theoretical analysis on the lower bound of the minimal intersample time. Finally, the applications to an aircraft dynamics and a robot arm plant are carried out to verify the efficient performance of the present novel design method.
A supervised machine learning estimator for the non-linear matter power spectrum - SEMPS
Mohammed, Irshad
2015-01-01
In this article, we argue that models based on machine learning (ML) can be very effective in estimating the non-linear matter power spectrum ($P(k)$). We employ the prediction ability of the supervised ML algorithms to build an estimator for the $P(k)$. The estimator is trained on a set of cosmological models, and redshifts for which the $P(k)$ is known, and it learns to predict $P(k)$ for any other set. We review three ML algorithms -- Random Forest, Gradient Boosting Machines, and K-Nearest Neighbours -- and investigate their prime parameters to optimize the prediction accuracy of the estimator. We also compute an optimal size of the training set, which is realistic enough, and still yields high accuracy. We find that, employing the optimal values of the internal parameters, a set of $50-100$ cosmological models is enough to train the estimator that can predict the $P(k)$ for a wide range of cosmological models, and redshifts. Using this configuration, we build a blackbox -- Supervised Estimator for Matter...
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
Bayram Sahin
2008-11-01
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ($lcK$ manifolds). We show that if a Riemannian holomorphic map between $lcK$ manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the $lcK$ manifold is Kaehler. Then we find similar results for Riemannian maps between $lcK$ manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.
Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions
Szlam, Arthur D.; Maggioni, Mauro; Coifman, Ronald R.; Bremer, James C., Jr.
2005-08-01
Classically, analysis on manifolds and graphs has been based on the study of the eigenfunctions of the Laplacian and its generalizations. These objects from differential geometry and analysis on manifolds have proven useful in applications to partial differential equations, and their discrete counterparts have been applied to optimization problems, learning, clustering, routing and many other algorithms.1-7 The eigenfunctions of the Laplacian are in general global: their support often coincides with the whole manifold, and they are affected by global properties of the manifold (for example certain global topological invariants). Recently a framework for building natural multiresolution structures on manifolds and graphs was introduced, that greatly generalizes, among other things, the construction of wavelets and wavelet packets in Euclidean spaces.8,9 This allows the study of the manifold and of functions on it at different scales, which are naturally induced by the geometry of the manifold. This construction proceeds bottom-up, from the finest scale to the coarsest scale, using powers of a diffusion operator as dilations and a numerical rank constraint to critically sample the multiresolution subspaces. In this paper we introduce a novel multiscale construction, based on a top-down recursive partitioning induced by the eigenfunctions of the Laplacian. This yields associated local cosine packets on manifolds, generalizing local cosines in Euclidean spaces.10 We discuss some of the connections with the construction of diffusion wavelets. These constructions have direct applications to the approximation, denoising, compression and learning of functions on a manifold and are promising in view of applications to problems in manifold approximation, learning, dimensionality reduction.
Tajima, Satohiro; Watanabe, Masataka
2011-03-01
We propose a two-stage learning method which implements occluded visual scene analysis into a generative model, a type of hierarchical neural network with bi-directional synaptic connections. Here, top-down connections simulate forward optics to generate predictions for sensory driven low-level representation, whereas bottom-up connections function to send the prediction error, the difference between the sensory based and the predicted low-level representation, to higher areas. The prediction error is then used to update the high-level representation to obtain better agreement with the visual scene. Although the actual forward optics is highly nonlinear and the accuracy of simulated forward optics is crucial for these types of models, the majority of previous studies have only investigated linear and simplified cases of forward optics. Here we take occluded vision as an example of nonlinear forward optics, where an object in front completely masks out the object behind. We propose a two-staged learning method inspired by the staged development of infant visual capacity. In the primary learning stage, a minimal set of object basis is acquired within a linear generative model using the conventional unsupervised learning scheme. In the secondary learning stage, an auxiliary multi-layer neural network is trained to acquire nonlinear forward optics by supervised learning. The important point is that the high-level representation of the linear generative model serves as the input and the sensory driven low-level representation provides the desired output. Numerical simulations show that occluded visual scene analysis can indeed be implemented by the proposed method. Furthermore, considering the format of input to the multi-layer network and analysis of hidden-layer units leads to the prediction that whole object representation of partially occluded objects, together with complex intermediate representation as a consequence of nonlinear transformation from non-occluded to
Space time manifolds and contact structures
Directory of Open Access Journals (Sweden)
K. L. Duggal
1990-01-01
Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.
Higher Order Hessian Structures on Manifolds
Indian Academy of Sciences (India)
R David Kumar
2005-08-01
In this paper we define th order Hessian structures on manifolds and study them. In particular, when =3, we make a detailed study and establish a one-to-one correspondence between third-order Hessian structures and a certain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.
Loops in Reeb Graphs of 2-Manifolds
Energy Technology Data Exchange (ETDEWEB)
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2004-12-16
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.
Loops in Reeb Graphs of 2-Manifolds
Energy Technology Data Exchange (ETDEWEB)
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
2003-02-11
Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
Gorban, A N
2010-01-01
We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.
The Chaotic Attractor Analysis of DJIA Based on Manifold Embedding and Laplacian Eigenmaps
Directory of Open Access Journals (Sweden)
Xiaohua Song
2016-01-01
Full Text Available By using the techniques of Manifold Embedding and Laplacian Eigenmaps, a novel strategy has been proposed in this paper to detect the chaos of Dow Jones Industrial Average. Firstly, the chaotic attractor of financial time series is assumed to lie on a low-dimensional manifold that is embedded into a high-dimensional Euclidean space. Then, an improved phase space reconstruction method and a nonlinear dimensionality reduction method are introduced to help reveal the structure of the chaotic attractor. Next, the empirical study on the financial time series of Dow Jones Industrial Average shows that there exists an attractor which lies on a manifold constructed by the time sequence of Moving average convergence divergence; finally, Determinism Test, Poincaré section, and translation analysis are used as test approaches to prove both whether it is a chaos and how it works.
Mielke, Alexander
1991-01-01
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists,...
Gorban, A N
2008-01-01
Principal manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Recently, methods for constructing non-linear principal manifolds were proposed, including our elastic maps approach which is based on a physical analogy with elastic membranes. We have developed a general geometric framework for constructing ``principal objects'' of various dimensions and topologies with the simplest quadratic form of the smoothness penalty which allows very effective parallel implementations. Our approach is implemented in three programming languages (C++, Java and Delphi) with two graphical user interfaces (VidaExpert http://bioinfo.curie.fr/projects/vidaexpert and ViMiDa http://bioinfo-out.curie.fr/projects/vimida applications). In this paper we overview the method of elastic maps and present in detail one of its major applications: the visuali...
Stable Myoelectric Control of a Hand Prosthesis using Non-Linear Incremental Learning
Directory of Open Access Journals (Sweden)
Arjan eGijsberts
2014-02-01
Full Text Available Stable myoelectric control of hand prostheses remains an open problem. The only successful human-machine interface is surface electromyography, typically allowing control of a few degrees of freedom. Machine learning techniques may have the potential to remove these limitations, but their performance is thus far inadequate: myoelectric signals change over time under the influence of various factors, deteriorating control performance. It is therefore necessary, in the standard approach, to regularly retrain a new model from scratch.We hereby propose a non-linear incremental learning method in which occasional updates with a modest amount of novel training data allow continual adaptation to the changes in the signals. In particular, Incremental Ridge Regression and an approximation of the Gaussian Kernel known as Random Fourier Features are combined to predict finger forces from myoelectric signals, both finger-by-finger and grouped in grasping patterns.We show that the approach is effective and practically applicable to this problem by first analyzing its performance while predicting single-finger forces. Surface electromyography and finger forces were collected from 10 intact subjects during four sessions spread over two different days; the results of the analysis show that small incremental updates are indeed effective to maintain a stable level of performance.Subsequently, we employed the same method on-line to teleoperate a humanoid robotic arm equipped with a state-of-the-art commercial prosthetic hand. The subject could reliably grasp, carry and release everyday-life objects, enforcing stable grasping irrespective of the signal changes, hand/arm movements and wrist pronation and supination.
Stable myoelectric control of a hand prosthesis using non-linear incremental learning
Gijsberts, Arjan; Bohra, Rashida; Sierra González, David; Werner, Alexander; Nowak, Markus; Caputo, Barbara; Roa, Maximo A.; Castellini, Claudio
2014-01-01
Stable myoelectric control of hand prostheses remains an open problem. The only successful human–machine interface is surface electromyography, typically allowing control of a few degrees of freedom. Machine learning techniques may have the potential to remove these limitations, but their performance is thus far inadequate: myoelectric signals change over time under the influence of various factors, deteriorating control performance. It is therefore necessary, in the standard approach, to regularly retrain a new model from scratch. We hereby propose a non-linear incremental learning method in which occasional updates with a modest amount of novel training data allow continual adaptation to the changes in the signals. In particular, Incremental Ridge Regression and an approximation of the Gaussian Kernel known as Random Fourier Features are combined to predict finger forces from myoelectric signals, both finger-by-finger and grouped in grasping patterns. We show that the approach is effective and practically applicable to this problem by first analyzing its performance while predicting single-finger forces. Surface electromyography and finger forces were collected from 10 intact subjects during four sessions spread over two different days; the results of the analysis show that small incremental updates are indeed effective to maintain a stable level of performance. Subsequently, we employed the same method on-line to teleoperate a humanoid robotic arm equipped with a state-of-the-art commercial prosthetic hand. The subject could reliably grasp, carry and release everyday-life objects, enforcing stable grasping irrespective of the signal changes, hand/arm movements and wrist pronation and supination. PMID:24616697
Stable myoelectric control of a hand prosthesis using non-linear incremental learning.
Gijsberts, Arjan; Bohra, Rashida; Sierra González, David; Werner, Alexander; Nowak, Markus; Caputo, Barbara; Roa, Maximo A; Castellini, Claudio
2014-01-01
Stable myoelectric control of hand prostheses remains an open problem. The only successful human-machine interface is surface electromyography, typically allowing control of a few degrees of freedom. Machine learning techniques may have the potential to remove these limitations, but their performance is thus far inadequate: myoelectric signals change over time under the influence of various factors, deteriorating control performance. It is therefore necessary, in the standard approach, to regularly retrain a new model from scratch. We hereby propose a non-linear incremental learning method in which occasional updates with a modest amount of novel training data allow continual adaptation to the changes in the signals. In particular, Incremental Ridge Regression and an approximation of the Gaussian Kernel known as Random Fourier Features are combined to predict finger forces from myoelectric signals, both finger-by-finger and grouped in grasping patterns. We show that the approach is effective and practically applicable to this problem by first analyzing its performance while predicting single-finger forces. Surface electromyography and finger forces were collected from 10 intact subjects during four sessions spread over two different days; the results of the analysis show that small incremental updates are indeed effective to maintain a stable level of performance. Subsequently, we employed the same method on-line to teleoperate a humanoid robotic arm equipped with a state-of-the-art commercial prosthetic hand. The subject could reliably grasp, carry and release everyday-life objects, enforcing stable grasping irrespective of the signal changes, hand/arm movements and wrist pronation and supination.
The Hodge theory of projective manifolds
de Cataldo, Mark Andrea
2007-01-01
This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
A Class of Homogeneous Einstein Manifolds
Institute of Scientific and Technical Information of China (English)
Yifang KANG; Ke LIANG
2006-01-01
A Riemannian manifold (M,g) is called Einstein manifold if its Ricci tensor satisfies r=c·g for some constant c. General existence results are hard to obtain,e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.
Branched standard spines of 3-manifolds
Benedetti, Riccardo
1997-01-01
This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.
CURVATURE COMPUTATIONS OF 2-MANIFOLDS IN IRk
Institute of Scientific and Technical Information of China (English)
Guo-liang Xu; Chandrajit L. Bajaj
2003-01-01
In this paper, we provide simple and explicit formulas for computing Riemannian cur-vatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k ≥ 3.
3-manifold groups are virtually residually p
Aschenbrenner, Matthias
2010-01-01
Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually $p$ for all but finitely many $p$. In particular, fundamental groups of hyperbolic $3$-manifolds are virtually residually $p$. It is also well-known that fundamental groups of $3$-manifolds are residually finite. In this paper we prove a common generalization of these results: every $3$-manifold group is virtually residually $p$ for all but finitely many~$p$. This gives evidence for the conjecture (Thurston) that fundamental groups of $3$-manifolds are linear groups.
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Cohomogeneity Two Actions on Flat Riemannian Manifolds
Institute of Scientific and Technical Information of China (English)
R. MIRZAIE
2007-01-01
In this paper, we study fiat Riemannian manifolds which have codimension two orbits,under the action of a closed and connected Lie group G of isometries. We assume that G has fixedpoints, then characterize M and orbits of M.
Yang, Qinmin; Jagannathan, Sarangapani
2012-04-01
In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.
Mathematical Background of Formalism of Operator Manifold
Ter-Kazarian, G T
1997-01-01
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The nature of operator manifold provides its elements with both quantum field and geometry aspects, a detailed study of which is a subject of present paper. It yields a quantization of geometry differing in principle from all earlier suggested schemes.
The convexity radius of a Riemannian manifold
Dibble, James
2014-01-01
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.
Multiply manifolded molten carbonate fuel cells
Energy Technology Data Exchange (ETDEWEB)
Krumpelt, M.; Roche, M.F.; Geyer, H.K.; Johnson, S.A.
1994-08-01
This study consists of research and development activities related to the concept of a molten carbonate fuel cell (MCFC) with multiple manifolds. Objective is to develop an MCFC having a higher power density and a longer life than other MCFC designs. The higher power density will result from thinner gas flow channels; the extended life will result from reduced temperature gradients. Simplification of the gas flow channels and current collectors may also significantly reduce cost for the multiply manifolded MCFC.
Blowing up generalized Kahler 4-manifolds
Cavalcanti, Gil R
2011-01-01
We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.
On some applications of invariant manifolds
Institute of Scientific and Technical Information of China (English)
Xi-Yun Hou; Lin Liu; Yu-Hui Zhao
2011-01-01
Taking transfer orbits of a collinear libration point probe, a lunar probe and an interplanetary probe as examples, some applications of stable and unstable invariant manifolds of the restricted three-body problem are discussed. Research shows that transfer energy is not necessarily conserved when invariant manifolds are used. For the cases in which the transfer energy is conserved, the cost is a much longer transfer time.
Sha, Daohang
2010-01-01
Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive algorithm is presented for online learning based on matrix operation and optimization methods analytically, which can avoid the trouble to select a proper learning rate for the gradient method. The proof of weak convergence of the proposed algorithm also is given. Although this approach is proposed for three-layer, feed-forward neural networks, it could be extended to multiple layer feed-forward neural networks. The effectiveness of the proposed algorithms applied to the identification of behavior of a two-input and two-output non-linear dynamic system is demonstrated by simulation experiments.
Quaternionic-like manifolds and homogeneous twistor spaces.
Pantilie, Radu
2016-12-01
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the 'quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the ρ-quaternionic manifolds. Moreover, the notion of 'heaven space' finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ-quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.
Robinson manifolds and Cauchy-Riemann spaces
Trautman, A
2002-01-01
A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...
Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang
2017-09-01
Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.
van der Schaaf, Marieke E; Warmerdam, Eveline; Crone, Eveline A; Cools, Roshan
2011-10-01
Abnormalities in value-based decision making during adolescence have often been attributed to non-linear, inverted-U shaped development of reward-related processes. This hypothesis is strengthened by functional imaging work revealing an inverted-U shaped relationship between age and reward-related activity in the striatum. However, behavioural studies have mostly reported linear rather than non-linear increases in reward-related performance. In the present study, we investigated the mechanisms underlying the development of reward- and punishment-related processing across four age groups using a reversal learning task previously shown to depend on striatal dopamine. We demonstrate both linear and non-linear age effects on distinct components of reversal learning. Specifically, results revealed a linear shift with age in terms of valence-dependent reversal learning, with children exhibiting better punishment than reward reversal learning, adults exhibiting better reward than punishment reversal learning and adolescents exhibiting an intermediate performance pattern. In addition, we also observed a non-linear, inverted-U shaped relationship between age and valence-independent reversal learning, which was due to aberrant ability of adolescents to update behaviour in response to negative performance feedback. These findings indicate that the (linear or nonlinear) nature of the relationship between age and reward learning depends on the type of reward learning under study.
Directory of Open Access Journals (Sweden)
Shandilya Sharad
2012-10-01
Full Text Available Abstract Background Ventricular Fibrillation (VF is a common presenting dysrhythmia in the setting of cardiac arrest whose main treatment is defibrillation through direct current countershock to achieve return of spontaneous circulation. However, often defibrillation is unsuccessful and may even lead to the transition of VF to more nefarious rhythms such as asystole or pulseless electrical activity. Multiple methods have been proposed for predicting defibrillation success based on examination of the VF waveform. To date, however, no analytical technique has been widely accepted. We developed a unique approach of computational VF waveform analysis, with and without addition of the signal of end-tidal carbon dioxide (PetCO2, using advanced machine learning algorithms. We compare these results with those obtained using the Amplitude Spectral Area (AMSA technique. Methods A total of 90 pre-countershock ECG signals were analyzed form an accessible preshosptial cardiac arrest database. A unified predictive model, based on signal processing and machine learning, was developed with time-series and dual-tree complex wavelet transform features. Upon selection of correlated variables, a parametrically optimized support vector machine (SVM model was trained for predicting outcomes on the test sets. Training and testing was performed with nested 10-fold cross validation and 6–10 features for each test fold. Results The integrative model performs real-time, short-term (7.8 second analysis of the Electrocardiogram (ECG. For a total of 90 signals, 34 successful and 56 unsuccessful defibrillations were classified with an average Accuracy and Receiver Operator Characteristic (ROC Area Under the Curve (AUC of 82.2% and 85%, respectively. Incorporation of the end-tidal carbon dioxide signal boosted Accuracy and ROC AUC to 83.3% and 93.8%, respectively, for a smaller dataset containing 48 signals. VF analysis using AMSA resulted in accuracy and ROC AUC of 64
2009-01-01
Applied Analysis, vol. 2007, Article ID 45153, 14 pages, 2007. doi:10.1155/2007/45153 113 [47] Marc Vaillant and Joan Glauns, “Surface matching via...Adaptive manifold learning. NIPS, 2004. [70] J. Costa , A. Girotra and A.O. Hero, Estimating local intrinsic dimension with k- nearest neighbor
Directory of Open Access Journals (Sweden)
Morteza Pourmehdi
2016-04-01
Full Text Available In this manuscript, for the first time, a fractional-order manifold in a synergetic approach using a fractional order controller is introduced. Furtheremore, in the synergetic theory a macro variable is expended into a linear combination of state variables. An aim is to increase the convergence rate as well as time response of the whole closed loop system. Quality of the proposed controller is investigated to control and synchronize a nonlinear chaotic Coullet system in comparison with an integer order manifold synergetic controller. The stability of the proposed controller is proven using the Lyapunov method. In this regard stabilizing control effort is yielded. Simulation result confirm convergence of states towards zero. This is achieved through a control effort with fewer oscillations and lower amplitude of signls which confirm feasibility of the control effort in practice.KEYWORDS: synergetic control theory; fractional order system; synchronization; nonlinear chaotic Coullet system; chaos control
RELATIVE CAMERA POSE ESTIMATION METHOD USING OPTIMIZATION ON THE MANIFOLD
Directory of Open Access Journals (Sweden)
C. Cheng
2017-05-01
Full Text Available To solve the problem of relative camera pose estimation, a method using optimization with respect to the manifold is proposed. Firstly from maximum-a-posteriori (MAP model to nonlinear least squares (NLS model, the general state estimation model using optimization is derived. Then the camera pose estimation model is applied to the general state estimation model, while the parameterization of rigid body transformation is represented by Lie group/algebra. The jacobian of point-pose model with respect to Lie group/algebra is derived in detail and thus the optimization model of rigid body transformation is established. Experimental results show that compared with the original algorithms, the approaches with optimization can obtain higher accuracy both in rotation and translation, while avoiding the singularity of Euler angle parameterization of rotation. Thus the proposed method can estimate relative camera pose with high accuracy and robustness.
Lattice QCD on Non-Orientable Manifolds
Mages, Simon; Borsanyi, Szabolcs; Fodor, Zoltan; Katz, Sandor; Szabo, Kalman K
2015-01-01
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the field configuration space becomes connected. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance completely. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to...
New Spinor Fields on Lorentzian 7-Manifolds
Bonora, L
2016-01-01
This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. It extends to higher dimensions the so-called Lounesto spinor fields classification in Minkowski spacetime, which encompasses Dirac, Weyl, Majorana, and more generally flagpoles, flag-dipoles and dipole spinor fields. A generalized classification according to the bilinear covariants was previously studied on Euclidean 7-manifolds. It presents either just one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, by means of such spinors one can introduce a generalized current density which further serves...
Cork twisting exotic Stein 4-manifolds
Akbulut, Selman
2011-01-01
From any 4-dimensional oriented handlebody X without 3- and 4-handles and with $b_2\\geq 1$, we construct arbitrary many compact Stein 4-manifolds which are mutually homeomorphic but not diffeomorphic to each other, so that their topological invariants (their fundamental groups, homology groups, boundary homology groups, and intersection forms) coincide with those of X. We also discuss the induced contact structures on their boundaries. Furthermore, for any smooth 4-manifold pair (Z,Y) such that the complement $Z-\\textnormal{int}\\,Y$ is a handlebody without 3- and 4-handles and with $b_2\\geq 1$, we construct arbitrary many exotic embeddings of a compact 4-manifold Y' into Z, such that Y' has the same topological invariants as Y.
Unknotting tunnels in hyperbolic 3-manifolds
Adams, Colin
2012-01-01
An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions for it to be an unknotting tunnel. In particular, if the vertical geodesic corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at infinity is connected to a larger horoball by a lift of the vertical geodesic. Such a vertical geodesic with length less than ln(2) is then shown to be an unknotting tunnel.
Duality constructions from quantum state manifolds
Kriel, J N; Scholtz, F G
2015-01-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifol...
Roughly isometric minimal immersions into Riemannian manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
A given metric (length-) space $X$ (whether compact or not) is roughly isometric to any one of its Kanai graphs $G$, which in turn can be {\\em{geometrized}} by considering each edge of $G$ as a 1-dimensional manifold with an associated metric $g$ giving the 'correct' length of the edge. In this t......A given metric (length-) space $X$ (whether compact or not) is roughly isometric to any one of its Kanai graphs $G$, which in turn can be {\\em{geometrized}} by considering each edge of $G$ as a 1-dimensional manifold with an associated metric $g$ giving the 'correct' length of the edge....... In this talk we will mainly be concerned with {\\em{minimal}} isometric immersions of such geometrized approximations $(G, g)$ of $X$ into Riemannian manifolds $N$ with bounded curvature. When such an immersion exists, we will call it an $X$-web in $N$. Such webs admit a natural 'geometric' extension...
Energy Technology Data Exchange (ETDEWEB)
DRIESSEN,BRIAN JAMES; SADEGH,NADER; KWOK,KWAN S.
2000-10-20
In this paper an optimization-based method of drift prevention is presented for learning control of underdetermined linear and weakly nonlinear time-varying dynamic systems. By defining a fictitious cost function and the associated model-based sub-optimality conditions, a new set of equations results, whose solution is unique, thus preventing large drifts from the initial input. Moreover, in the limiting case where the modeling error approaches zero, the input that the proposed method converges to is the unique feasible (zero error) input that minimizes the fictitious cost function, in the linear case, and locally minimizes it in the (weakly) nonlinear case. Otherwise, under mild restrictions on the modeling error, the method converges to a feasible sub-optimal input.
Hosseinifard, Behshad; Moradi, Mohammad Hassan; Rostami, Reza
2013-03-01
Diagnosing depression in the early curable stages is very important and may even save the life of a patient. In this paper, we study nonlinear analysis of EEG signal for discriminating depression patients and normal controls. Forty-five unmedicated depressed patients and 45 normal subjects were participated in this study. Power of four EEG bands and four nonlinear features including detrended fluctuation analysis (DFA), higuchi fractal, correlation dimension and lyapunov exponent were extracted from EEG signal. For discriminating the two groups, k-nearest neighbor, linear discriminant analysis and logistic regression as the classifiers are then used. Highest classification accuracy of 83.3% is obtained by correlation dimension and LR classifier among other nonlinear features. For further improvement, all nonlinear features are combined and applied to classifiers. A classification accuracy of 90% is achieved by all nonlinear features and LR classifier. In all experiments, genetic algorithm is employed to select the most important features. The proposed technique is compared and contrasted with the other reported methods and it is demonstrated that by combining nonlinear features, the performance is enhanced. This study shows that nonlinear analysis of EEG can be a useful method for discriminating depressed patients and normal subjects. It is suggested that this analysis may be a complementary tool to help psychiatrists for diagnosing depressed patients. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Decision Manifold Approximation for Physics-Based Simulations
Wong, Jay Ming; Samareh, Jamshid A.
2016-01-01
With the recent surge of success in big-data driven deep learning problems, many of these frameworks focus on the notion of architecture design and utilizing massive databases. However, in some scenarios massive sets of data may be difficult, and in some cases infeasible, to acquire. In this paper we discuss a trajectory-based framework that quickly learns the underlying decision manifold of binary simulation classifications while judiciously selecting exploratory target states to minimize the number of required simulations. Furthermore, we draw particular attention to the simulation prediction application idealized to the case where failures in simulations can be predicted and avoided, providing machine intelligence to novice analysts. We demonstrate this framework in various forms of simulations and discuss its efficacy.
Manifold-Ranking-Based Keyword Propagation for Image Retrieval
Directory of Open Access Journals (Sweden)
Li Mingjing
2006-01-01
Full Text Available A novel keyword propagation method is proposed for image retrieval based on a recently developed manifold-ranking algorithm. In contrast to existing methods which train a binary classifier for each keyword, our keyword model is constructed in a straightforward manner by exploring the relationship among all images in the feature space in the learning stage. In relevance feedback, the feedback information can be naturally incorporated to refine the retrieval result by additional propagation processes. In order to speed up the convergence of the query concept, we adopt two active learning schemes to select images during relevance feedback. Furthermore, by means of keyword model update, the system can be self-improved constantly. The updating procedure can be performed online during relevance feedback without extra offline training. Systematic experiments on a general-purpose image database consisting of 5 000 Corel images validate the effectiveness of the proposed method.
Burning invariant manifolds in reactive front propagation
Mahoney, John; Mitchell, Kevin; Solomon, Tom
2011-01-01
We present theory and experiments on the dynamics of reaction fronts in a two-dimensional flow composed of a chain of alternating vortices. Inspired by the organization of passive transport by invariant manifolds, we introduce burning invariant manifolds (BIMs), which act as one-sided barriers to front propagation. The BIMs emerge from the theory when the advection-reaction- diffusion system is recast as an ODE for reaction front elements. Experimentally, we demonstrate how these BIMs can be measured and compare their behavior with simulation. Finally, a topological BIM formalism yields a maximum front propagation speed.
The "Parity" Anomaly On An Unorientable Manifold
Witten, Edward
2016-01-01
The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. The "parity" anomaly has traditionally been studied on orientable manifolds only, but recent developments involving topological superconductors have made it clear that one can get more information by asking what happens on an unorientable manifold. In this paper, we analyze the "parity" anomaly for fermions coupled to gauge fields and gravity in $2+1$ dimensions. We consider applications to gapped boundary states of a topological superconductor and to M2-branes in string/M-theory.
Wilson Fermions on a Randomly Triangulated Manifold
Burda, Z; Krzywicki, A
1999-01-01
A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2-d, on an arbitrary orientable manifold without boundary. It can be easily converted into a computer code. The equivalence, on a sphere, of Majorana fermions and Ising spins in 2-d is rederived. The method can, in principle, be extended to higher dimensions.
Tangent bundles of Hantzsche-Wendt manifolds
Gaşior, A.; Szczepański, A.
2013-08-01
We formulate a condition for the existence of a SpinC-structure on an oriented flat manifold Mn with H2(Mn,R)=0. We prove that Mn has a SpinC-structure if and only if there exists a homomorphism ɛ:π1(Mn)→SpinC(n) such that λ∘ɛ=h, where h:π1(Mn)→SO(n) is a holonomy homomorphism and λ:SpinC(n)→SO(n) is a standard homomorphism defined. As an application we shall prove that all cyclic Hantzsche-Wendt manifolds do not have the SpinC-structure.
Beyond Sentiment: The Manifold of Human Emotions
Kim, Seungyeon; Lebanon, Guy; Essa, Irfan
2012-01-01
Sentiment analysis predicts the presence of positive or negative emotions in a text document. In this paper we consider higher dimensional extensions of the sentiment concept, which represent a richer set of human emotions. Our approach goes beyond previous work in that our model contains a continuous manifold rather than a finite set of human emotions. We investigate the resulting model, compare it to psychological observations, and explore its predictive capabilities. Besides obtaining significant improvements over a baseline without manifold, we are also able to visualize different notions of positive sentiment in different domains.
Microlocal properties of scattering matrices for Schr\\"odinger equations on scattering manifolds
Ito, Kenichi
2011-01-01
Let $M$ be a scattering manifold, i.e., a Riemannian manifold with asymptotically conic structure, and let $H$ be a Schr\\"odinger operator on $M$. We can construct a natural time-dependent scattering theory for $H$ with a suitable reference system, and the scattering matrix is defined accordingly. We here show the scattering matrices are Fourier integral operators associated to a canonical transform on the boundary manifold generated by the geodesic flow. In particular, we learn that the wave front sets are mapped according to the canonical transform. These results are generalizations of a theorem by Melrose and Zworski, but the framework and the proof are quite different. These results may be considered as generalizations or refinements of the classical off-diagonal smoothness of the scattering matrix for 2-body quantum scattering on Euclidean spaces.
Improving head and body pose estimation through semi-supervised manifold alignment
Heili, Alexandre
2014-10-27
In this paper, we explore the use of a semi-supervised manifold alignment method for domain adaptation in the context of human body and head pose estimation in videos. We build upon an existing state-of-the-art system that leverages on external labelled datasets for the body and head features, and on the unlabelled test data with weak velocity labels to do a coupled estimation of the body and head pose. While this previous approach showed promising results, the learning of the underlying manifold structure of the features in the train and target data and the need to align them were not explored despite the fact that the pose features between two datasets may vary according to the scene, e.g. due to different camera point of view or perspective. In this paper, we propose to use a semi-supervised manifold alignment method to bring the train and target samples closer within the resulting embedded space. To this end, we consider an adaptation set from the target data and rely on (weak) labels, given for example by the velocity direction whenever they are reliable. These labels, along with the training labels are used to bias the manifold distance within each manifold and to establish correspondences for alignment.
Nonlinear Model Predictive Control of A Gasoline HCCI Engine Using Extreme Learning Machines
Janakiraman, Vijay Manikandan; Nguyen, XuanLong; Assanis, Dennis
2015-01-01
Homogeneous charge compression ignition (HCCI) is a futuristic combustion technology that operates with a high fuel efficiency and reduced emissions. HCCI combustion is characterized by complex nonlinear dynamics which necessitates a model based control approach for automotive application. HCCI engine control is a nonlinear, multi-input multi-output problem with state and actuator constraints which makes controller design a challenging task. Typical HCCI controllers make use of a first princi...
Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries
Sargsyan, Syuzanna; Brunton, Steven L.; Kutz, J. Nathan
2015-09-01
We demonstrate the synthesis of sparse sampling and dimensionality reduction to characterize and model nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper orthogonal decomposition in order to expose the dominant low-rank coherent structures. Here, libraries of the nonlinear terms are also constructed in order to take advantage of the discrete empirical interpolation method and projection that allows for the approximation of nonlinear terms from a sparse number of grid points. The selected grid points are shown to be effective sensing and measurement locations for characterizing the underlying dynamics, stability, and bifurcations of nonlinear dynamical systems. The use of empirical interpolation points and sparse representation facilitates a family of local reduced-order models for each physical regime, rather than a higher-order global model, which has the benefit of physical interpretability of energy transfer between coherent structures. The method advocated also allows for orders-of-magnitude improvement in computational speed and memory requirements. To illustrate the method, the discrete interpolation points and nonlinear modal libraries are used for sparse representation in order to classify and reconstruct the dynamic bifurcation regimes in the complex Ginzburg-Landau equation. It is also shown that point measurements of the nonlinearity are more effective than linear measurements when sensor noise is present.
On Kähler–Norden Manifolds-Erratum
Indian Academy of Sciences (India)
M Iscan; A A Salimov
2009-02-01
This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.
The influence of learning and updating speed on the growth of commercial websites
Wan, Xiaoji; Deng, Guishi; Bai, Yang; Xue, Shaowei
2012-08-01
In this paper, we study the competition model of commercial websites with learning and updating speed, and further analyze the influence of learning and updating speed on the growth of commercial websites from a nonlinear dynamics perspective. Using the center manifold theory and the normal form method, we give the explicit formulas determining the stability and periodic fluctuation of commercial sites. Numerical simulations reveal that sites periodically fluctuate as the speed of learning and updating crosses one threshold. The study provides reference and evidence for website operators to make decisions.
$\\rm G_2$ holonomy manifolds are superconformal
Díaz, Lázaro O Rodríguez
2016-01-01
We study the chiral de Rham complex (CDR) over a manifold $M$ with holonomy $\\rm G_2$. We prove that the vertex algebra of global sections of the CDR associated to $M$ contains two commuting copies of the Shatashvili-Vafa $\\rm G_2$ superconformal algebra. Our proof is a tour de force, based on explicit computations.
Four-manifolds, geometries and knots
Hillman, Jonathan A
2007-01-01
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...
Einstein constraints on n dimensional compact manifolds
Choquet-Bruhat, Y
2004-01-01
We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions with unscaled sources.
Becker, Katrin; Robbins, Daniel
2015-01-01
In this talk we report on recent progress in describing compactifications of string theory and M-theory on G_2 and Spin(7) manifolds. We include the infinite set of alpha'-corrections and describe the entire tower of massless and massive Kaluza-Klein modes resulting from such compactifications.
Remarks on homogeneous manifolds satisfying Levi conditions
Huckleberry, Alan
2010-01-01
Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in some detail. A precise classification of pseudoconvex flag domains is given. It is shown that flag domains which are in a certain sense generic are pseudoconcave.
Exponential estimates of symplectic slow manifolds
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Wulff, C.
2016-01-01
is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman...
Modelling of the Manifold Filling Dynamics
DEFF Research Database (Denmark)
Hendricks, Elbert; Chevalier, Alain Marie Roger; Jensen, Michael
1996-01-01
Mean Value Engine Models (MVEMs) are dynamic models which describe dynamic engine variable (or state) responses on time scales slightly longer than an engine event. This paper describes a new model of the intake manifold filling dynamics which is simple and easy to calibrate for use in engine con...
Duality constructions from quantum state manifolds
Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.
2015-11-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.
Heat Kernel Renormalization on Manifolds with Boundary
Albert, Benjamin I.
2016-01-01
In the monograph Renormalization and Effective Field Theory, Costello gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. In this paper, we extend Costello's renormalization procedure to a class of manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Geometrical description of denormalized thermodynamic manifold
Institute of Scientific and Technical Information of China (English)
Wu Li-Ping; Sun Hua-Fei; Cao Li-Mei
2009-01-01
In view of differential geometry,the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.
On homological stability for configuration spaces on closed background manifolds
Cantero, Federico; Palmer, Martin
2014-01-01
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the background manifold is closed, in which case the classical stabilisation map does not exist. We then establish conditions on the manifold and on the coefficients under which homological stability holds for configuration spaces on closed manifolds. These conditio...
Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds
Ivashkovich, S
2011-01-01
We prove the Royden's Lemma for complex Hilbert manifolds, i.e., that a holomorphic imbedding of the closure of a finite dimensional, strictly pseudoconvex domain into a complex Hilbert manifold extends to a biholomorphic mapping onto a product of this domain with the unit ball in Hilbert space. This reduces several problems concerning complex Hilbert manifolds to open subsets of a Hilbert space. As an illustration we prove some results on generalized loop spaces of complex manifolds.
Fluid manifold design for a solar energy storage tank
Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.
1975-01-01
A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.
Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai
2015-07-01
The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.
A Critical Centre-Stable Manifold for the Schroedinger Equation in Three Dimensions
Beceanu, Marius
2009-01-01
Consider the H^{1/2}-critical Schroedinger equation with a cubic nonlinearity in R^3, i \\partial_t \\psi + \\Delta \\psi + |\\psi|^2 \\psi = 0. It admits an eight-dimensional manifold of periodic solutions called solitons e^{i(\\Gamma + vx - t|v|^2 + \\alpha^2 t)} \\phi(x-2tv-D, \\alpha), where \\phi(x, \\alpha) is a positive ground state solution of the semilinear elliptic equation -\\Delta \\phi + \\alpha^2\\phi = \\phi^3. We prove that in the neighborhood of the soliton manifold there exists a H^{1/2} real analytic manifold N of asymptotically stable solutions of the Schroedinger equation, meaning they are the sum of a moving soliton and a dispersive term. Furthermore, a solution starting on N remains on N for all positive time and for some finite negative time and N can be identified as the centre-stable manifold for this equation. The proof is based on the method of modulation, introduced by Soffer and Weinstein and adapted by Schlag to the L^2-supercritical case. Novel elements include a different linearization and a S...
On Self-Mapping Degrees of S3- Geometry Manifolds
Institute of Scientific and Technical Information of China (English)
Xiao Ming DU
2009-01-01
In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston's picture.
Canonical connection on a class of Riemannian almost product manifolds
Mekerov, Dimitar
2009-01-01
The canonical connection on a Riemannian almost product manifolds is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with nonintegrable almost product structure.
NUMERICAL MANIFOLD METHOD AND ITS APPLICATION IN UNDERGROUND POENINGS
Institute of Scientific and Technical Information of China (English)
王芝银; 李云鹏
1998-01-01
A brief introduction is made for the Numerical Manifold Method and its analysingprocess in rock mechanics. Some aspects of the manifold method are improved in implementingprocess according to the practice of excavating underground openings. Corresponding formulasare given and a computer program of the Numerical Manifold Method has been completed in thispaper.
Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
Biswas, Indranil; 10.1016/j.difgeo.2009.09.003
2010-01-01
We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\\"ahler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.
Wave equations on anti self dual (ASD) manifolds
Bashingwa, Jean-Juste; Kara, A. H.
2017-06-01
In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.
Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
Directory of Open Access Journals (Sweden)
Yvette Kosmann-Schwarzbach
2008-01-01
Full Text Available After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.
Local topology in deformation spaces of hyperbolic 3-manifolds
Brock, Jeffrey F; Canary, Richard D; Minsky, Yair N
2009-01-01
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar results are obtained for deformation spaces of acylindrical 3-manifolds and Bers slices.
On the conformal geometry of transverse Riemann Lorentz manifolds
Aguirre, E.; Fernández, V.; Lafuente, J.
2007-06-01
Physical reasons suggested in [J.B. Hartle, S.W. Hawking, Wave function of the universe, Phys. Rev. D41 (1990) 1815-1834] for the Quantum Gravity Problem lead us to study type-changing metrics on a manifold. The most interesting cases are Transverse Riemann-Lorentz Manifolds. Here we study the conformal geometry of such manifolds.
Einstein Metrics, Four-Manifolds, and Differential Topology
2004-01-01
This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of Riemannian variational problems on 4-manifolds.