SUPERCONVERGENCE OF LEAST-SQUARES MIXED FINITE ELEMENTS FOR ELLIPTIC PROBLEMS ON TRIANGULATION
Institute of Scientific and Technical Information of China (English)
陈艳萍; 杨菊娥
2003-01-01
In this paper,we present the least-squares mixed finite element method and investigate superconvergence phenomena for the second order elliptic boundary-value problems over triangulations.On the basis of the L2-projection and some mixed finite element projections,we obtain the superconvergence result of least-squares mixed finite element solutions.This error estimate indicates an accuracy of O(h3/2)if the lowest order Raviart-Thomas elements are employed.
LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
Dan-ping Yang
2002-01-01
Two least-squares mixed finite element schemes are formulated to solve the initialboundary value problem of a nonlinear parabolic partial differential equation and the convergence of these schemes are analyzed.
LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM
Institute of Scientific and Technical Information of China (English)
Lie-heng Wang; Huo-yuan Duan
2000-01-01
In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived.
SUPERCONVERGENCE OF LEAST-SQUARES MIXED FINITE ELEMENT FOR SECOND-ORDER ELLIPTIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
Yan-ping Chen; De-hao Yu
2003-01-01
In this paper the least-squares mixed finite element is considered for solving secondorder elliptic problems in two dimensional domains. The primary solution u and the flux σ are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection,superconvergent Hi-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(hr+2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-DouglasFortin-Marini elements of order r are employed with optimal error estimate of O(hr+1).
LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Shao-qin Gao
2005-01-01
Least-squares mixed finite element methods are proposed and analyzed for the incompressible magnetohydrodynamic equations, where the two vorticities are additionally introduced as independent variables in order that the primal equations are transformed into the first-order systems. We show that there hold the coerciveness and the optimal error bound in appropriate norms for all variables under consideration, which can be approximated by all kinds of continuous element. Consequently, the Babuska-Brezzi condition (i.e. the inf-sup condition) and the indefiniteness are avoided which are essential features of the classical mixed methods.
Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro
1989-01-01
Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.
Least-squares finite-element lattice Boltzmann method.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2004-06-01
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.
Institute of Scientific and Technical Information of China (English)
LUO Zhen-dong; MAO Yun-kui; ZHU Jiang
2007-01-01
The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented.And the existence and error estimates of its solution are derived. Through this method,the combination among the mixed finite element spaces does not demand the discrete Babu(s)ka-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.
A Least Square Finite Element Technique for Transonic Flow with Shock,
1977-08-22
dimensional form. A least square finite element technique was used with a linearly interpolating polynomial to reduce the governing equation to a...partial differential equations by a system of ordinary differential equations. Using the least square finite element technique a computer program was
A least squares finite element scheme for transonic flow around harmonically oscillating airfoils
Cox, C. L.; Fix, G. J.; Gunzburger, M. D.
1983-01-01
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.
Least-squares finite element discretizations of neutron transport equations in 3 dimensions
Energy Technology Data Exchange (ETDEWEB)
Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)
1996-12-31
The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.
A Coupled Finite Difference and Moving Least Squares Simulation of Violent Breaking Wave Impact
DEFF Research Database (Denmark)
Lindberg, Ole; Bingham, Harry B.; Engsig-Karup, Allan Peter
2012-01-01
Two model for simulation of free surface flow is presented. The first model is a finite difference based potential flow model with non-linear kinematic and dynamic free surface boundary conditions. The second model is a weighted least squares based incompressible and inviscid flow model. A special...... feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep...... and overturning wave impacts on a vertical breakwater. Wave groups with five different wave heights are propagated from offshore to the vicinity of the breakwater, where the waves are steep, but still smooth and non-overturning. These waves are used as initial condition for the weighted least squares based...
Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method
Directory of Open Access Journals (Sweden)
J. Amani
2014-01-01
Full Text Available The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.
Shimabukuro, Yosio Edemir; Smith, James A.
1991-01-01
Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.
A Coupled Finite Difference and Moving Least Squares Simulation of Violent Breaking Wave Impact
DEFF Research Database (Denmark)
Lindberg, Ole; Bingham, Harry B.; Engsig-Karup, Allan Peter
2012-01-01
incompressible and inviscid model and the wave impacts on the vertical breakwater are simulated in this model. The resulting maximum pressures and forces on the breakwater are relatively high when compared with other studies and this is due to the incompressible nature of the present model.......Two model for simulation of free surface flow is presented. The first model is a finite difference based potential flow model with non-linear kinematic and dynamic free surface boundary conditions. The second model is a weighted least squares based incompressible and inviscid flow model. A special...... feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep...
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.
The least square particle finite element method for simulating large amplitude sloshing flows
Institute of Scientific and Technical Information of China (English)
Bo Tang; Junfeng Li; Tianshu Wang
2008-01-01
Large amplitude sloshing in tanks is simulated by the least square particle finite element method (LSPFEM) in this paper: The least square finite element method (LSFEM) is employed to spatially discrete the Navier-Stokes equations, and to avoid the stabilization issues due to the incompressibility condition for equal-order interpolation of the velocity and the pressure, as usually used in Galerkin method to satisfy the well-known LBB condition. The LSPFEM also uses the Lagrangian description to model the motion of nodes (particles). A mesh which connects these nodes is constructed by a triangulation algorithm to avoid the mesh distortion. A quasi α-shapes algorithm is used to identify the free surface boundary. The nodes are viewed as particles which can freely move and even separate from the main fluid domain. Finally this method is used to study the large amplitude sloshing evolution in two dimensional tanks. The results are compared with those obtained by Flow-3d with good agreement.
A least-squares finite element method for 3D incompressible Navier-Stokes equations
Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
Mixed Least Square Method for Priority of Complementary Judgement Matrix and Its Algorithm
Institute of Scientific and Technical Information of China (English)
ZHOU Hong-an; LIU San-yang
2007-01-01
Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method (MLSM) for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., are introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.
Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J
2017-01-01
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.
Payette, G. S.; Reddy, J. N.
2011-05-01
In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L2 norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier-Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.
Smith, Bradford Scott, Jr.
The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation in elements downstream of a shock and having edges coincident with the shock showed a slight reduction in the solution error. However there was very little qualitative difference between solutions using polynomial and exponential interpolation. Regardless of the type of interpolation used, the shocks were smeared and oscillations were present both upstream and downstream of the shock waves. When a mesh adaptation scheme was implemented, exponential elements adjacent to the shock waves became much smaller and the numerical solution diverged. Changing the exponential elements to polynomial elements yielded a convergent solution. There appears to be no significant advantage to using exponential interpolation in comparison to Lagrange polynomial interpolation.
Large-scale computation of incompressible viscous flow by least-squares finite element method
Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.
Solution of shallow-water equations using least-squares finite-element method
Institute of Scientific and Technical Information of China (English)
Shin-Jye Liang; Jyh-Haw Tang; Ming-Shun Wu
2008-01-01
A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is pre-sented. The model is capable of handling complex topogra-phy, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include: (1) sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; (2) upwind scheme is no needed; (3) a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition; and (4) the resulting system of equations is sym-metric and positive-definite (SPD) which can be solved effi-ciently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylin-der and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.
Least-squares finite-element method for shallow-water equations with source terms
Institute of Scientific and Technical Information of China (English)
Shin-Jye Liang; Tai-Wen Hsu
2009-01-01
Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
Identifying differentially methylated genes using mixed effect and generalized least square models
Directory of Open Access Journals (Sweden)
Yan Pearlly S
2009-12-01
Full Text Available Abstract Background DNA methylation plays an important role in the process of tumorigenesis. Identifying differentially methylated genes or CpG islands (CGIs associated with genes between two tumor subtypes is thus an important biological question. The methylation status of all CGIs in the whole genome can be assayed with differential methylation hybridization (DMH microarrays. However, patient samples or cell lines are heterogeneous, so their methylation pattern may be very different. In addition, neighboring probes at each CGI are correlated. How these factors affect the analysis of DMH data is unknown. Results We propose a new method for identifying differentially methylated (DM genes by identifying the associated DM CGI(s. At each CGI, we implement four different mixed effect and generalized least square models to identify DM genes between two groups. We compare four models with a simple least square regression model to study the impact of incorporating random effects and correlations. Conclusions We demonstrate that the inclusion (or exclusion of random effects and the choice of correlation structures can significantly affect the results of the data analysis. We also assess the false discovery rate of different models using CGIs associated with housekeeping genes.
Kang, Gumin; Lee, Kwangchil; Park, Haesung; Lee, Jinho; Jung, Youngjean; Kim, Kyoungsik; Son, Boongho; Park, Hyoungkuk
2010-06-15
Mixed hydrofluoric and nitric acids are widely used as a good etchant for the pickling process of stainless steels. The cost reduction and the procedure optimization in the manufacturing process can be facilitated by optically detecting the concentration of the mixed acids. In this work, we developed a novel method which allows us to obtain the concentrations of hydrofluoric acid (HF) and nitric acid (HNO(3)) mixture samples with high accuracy. The experiments were carried out for the mixed acids which consist of the HF (0.5-3wt%) and the HNO(3) (2-12wt%) at room temperature. Fourier Transform Raman spectroscopy has been utilized to measure the concentration of the mixed acids HF and HNO(3), because the mixture sample has several strong Raman bands caused by the vibrational mode of each acid in this spectrum. The calibration of spectral data has been performed using the partial least squares regression method which is ideal for local range data treatment. Several figures of merit (FOM) were calculated using the concept of net analyte signal (NAS) to evaluate performance of our methodology.
Iterative least square phase-measuring method that tolerates extended finite bandwidth illumination.
Munteanu, Florin; Schmit, Joanna
2009-02-20
Iterative least square phase-measuring techniques address the phase-shifting interferometry issue of sensitivity to vibrations and scanner nonlinearity. In these techniques the wavefront phase and phase steps are determined simultaneously from a single set of phase-shifted fringe frames where the phase shift does not need to have a nominal value or be a priori precisely known. This method is commonly used in laser interferometers in which the contrast of fringes is constant between frames and across the field. We present step-by-step modifications to the basic iterative least square method. These modifications allow for vibration insensitive measurements in an interferometric system in which fringe contrast varies across a single frame, as well as from frame to frame, due to the limited bandwidth light source and the nonzero numerical aperture of the objective. We demonstrate the efficiency of the new algorithm with experimental data, and we analyze theoretically the degree of contrast variation that this new algorithm can tolerate.
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 王会军
2002-01-01
A nonlinear Galerkin/ Petrov- least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. The existence, uniqueness and convergence ( at optimal rate ) of the NGPLSME solution is proved in the case of sufficient viscosity ( or small data).
A semi-implicit finite strain shell algorithm using in-plane strains based on least-squares
Areias, P.; Rabczuk, T.; de Sá, J. César; Natal Jorge, R.
2015-04-01
The use of a semi-implicit algorithm at the constitutive level allows a robust and concise implementation of low-order effective shell elements. We perform a semi-implicit integration in the stress update algorithm for finite strain plasticity: rotation terms (highly nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the (in this case evolving) reference configuration and relative Green-Lagrange strains (quadratic) are used to account for change in the equilibrium configuration implicitly. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use a common configuration. A finite strain quadrilateral element with least-squares assumed in-plane shear strains (in curvilinear coordinates) and classical transverse shear assumed strains is introduced. It is an alternative to enhanced-assumed-strain (EAS) formulations and, contrary to this, produces an element satisfying ab-initio the Patch test. No additional degrees-of-freedom are present, contrasting with EAS. Least-squares fit allows the derivation of invariant finite strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. Two thickness parameters per node are adopted to reproduce the Poisson effect in bending. Metric components are fully deduced and exact linearization of the shell element is performed. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.
Institute of Scientific and Technical Information of China (English)
Jayantha Pasdunkorale A.; Ian W. Turner
2005-01-01
An unstructured mesh finite volume discretisation method for simulating diffusion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume finite-element method and it retains the local continuity of the flux at the control volume faces. A least squares function reconstruction technique together with a new flux decomposition strategy is used to obtain an accurate flux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it significantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes,and appears independent of the mesh quality.
A point cloud modeling method based on geometric constraints mixing the robust least squares method
Yue, JIanping; Pan, Yi; Yue, Shun; Liu, Dapeng; Liu, Bin; Huang, Nan
2016-10-01
The appearance of 3D laser scanning technology has provided a new method for the acquisition of spatial 3D information. It has been widely used in the field of Surveying and Mapping Engineering with the characteristics of automatic and high precision. 3D laser scanning data processing process mainly includes the external laser data acquisition, the internal industry laser data splicing, the late 3D modeling and data integration system. For the point cloud modeling, domestic and foreign researchers have done a lot of research. Surface reconstruction technology mainly include the point shape, the triangle model, the triangle Bezier surface model, the rectangular surface model and so on, and the neural network and the Alfa shape are also used in the curved surface reconstruction. But in these methods, it is often focused on single surface fitting, automatic or manual block fitting, which ignores the model's integrity. It leads to a serious problems in the model after stitching, that is, the surfaces fitting separately is often not satisfied with the well-known geometric constraints, such as parallel, vertical, a fixed angle, or a fixed distance. However, the research on the special modeling theory such as the dimension constraint and the position constraint is not used widely. One of the traditional modeling methods adding geometric constraints is a method combing the penalty function method and the Levenberg-Marquardt algorithm (L-M algorithm), whose stability is pretty good. But in the research process, it is found that the method is greatly influenced by the initial value. In this paper, we propose an improved method of point cloud model taking into account the geometric constraint. We first apply robust least-squares to enhance the initial value's accuracy, and then use penalty function method to transform constrained optimization problems into unconstrained optimization problems, and finally solve the problems using the L-M algorithm. The experimental results
Directory of Open Access Journals (Sweden)
Mohamed G. Egila
2016-12-01
Full Text Available This paper presents a proposed design for analyzing electrocardiography (ECG signals. This methodology employs highpass least-square linear phase Finite Impulse Response (FIR filtering technique to filter out the baseline wander noise embedded in the input ECG signal to the system. Discrete Wavelet Transform (DWT was utilized as a feature extraction methodology to extract the reduced feature set from the input ECG signal. The design uses back propagation neural network classifier to classify the input ECG signal. The system is implemented on Xilinx 3AN-XC3S700AN Field Programming Gate Array (FPGA board. A system simulation has been done. The design is compared with some other designs achieving total accuracy of 97.8%, and achieving reduction in utilizing resources on FPGA implementation.
Liu, Hongxu; Jiao, Xiangmin
2016-06-01
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.
Directory of Open Access Journals (Sweden)
Américo José dos Santos Reis
2005-01-01
Full Text Available By definition, the genetic effects obtained from a circulant diallel table are random. However, because of the methods of analysis, those effects have been considered as fixed. Two different statistical approaches were applied. One assumed the model to be fixed and obtained solutions through the ordinary least square (OLS method. The other assumed a mixed model and estimated the fixed effects (BLUE by generalized least squares (GLS and the best linear unbiased predictor (BLUP of the random effects. The goal of this study was to evaluate the consequences when considering these effects as fixed or random, using the coefficient of correlation between the responses of observed and non-observed hybrids. Crossings were made between S1 inbred lines from two maize populations developed at Universidade Federal de Goiás, the UFG-Samambaia "Dent" and UFG-Samambaia "Flint". A circulant inter-group design was applied, and there were five (s = 5 crossings for each parent. The predictions were made using a reduced model. Diallels with different sizes of s (from 2 to 5 were simulated, and the coefficients of correlation were obtained using two different approaches for each size of s. In the first approach, the observed hybrids were included in both the estimation of the genetic parameters and the coefficient of correlation, while in the second a cross-validation process was employed. In this process, the set of hybrids was divided in two groups: one group, comprising 75% of the original group, to estimate the genetic parameters, and a second one, consisting of the remaining 25%, to validate the predictions. In all cases, a bootstrap process with 200 resamplings was used to generate the empirical distribution of the correlation coefficient. This coefficient showed a decrease as the value of s decreased. The cross-validation method allowed to estimate the bias magnitude in evaluating the correlation coefficient using the same hybrids, to predict the genetic
Bayesian least squares deconvolution
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Bayesian least squares deconvolution
Ramos, A Asensio
2015-01-01
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
He, Qiaolin
2011-06-01
In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES
Institute of Scientific and Technical Information of China (English)
Plamen Y. Yalamov; Jin-yun Yuan
2003-01-01
A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems.The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to the solution fast for Toeplitz STLS problems. Since the method is designed for general TLS problems, other structured problems can be treated similarly.
AKLSQF - LEAST SQUARES CURVE FITTING
Kantak, A. V.
1994-01-01
The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.
Quasi-least squares regression
Shults, Justine
2014-01-01
Drawing on the authors' substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression-a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitu
Bayesian Sparse Partial Least Squares
Vidaurre, D.; Gerven, M.A.J. van; Bielza, C.; Larrañaga, P.; Heskes, T.M.
2013-01-01
Partial least squares (PLS) is a class of methods that makes use of a set of latent or unobserved variables to model the relation between (typically) two sets of input and output variables, respectively. Several flavors, depending on how the latent variables or components are computed, have been dev
Shakib, Farzin; Hughes, Thomas J. R.
1991-01-01
A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.
Abdi, Hervé; Williams, Lynne J
2013-01-01
Partial least square (PLS) methods (also sometimes called projection to latent structures) relate the information present in two data tables that collect measurements on the same set of observations. PLS methods proceed by deriving latent variables which are (optimal) linear combinations of the variables of a data table. When the goal is to find the shared information between two tables, the approach is equivalent to a correlation problem and the technique is then called partial least square correlation (PLSC) (also sometimes called PLS-SVD). In this case there are two sets of latent variables (one set per table), and these latent variables are required to have maximal covariance. When the goal is to predict one data table the other one, the technique is then called partial least square regression. In this case there is one set of latent variables (derived from the predictor table) and these latent variables are required to give the best possible prediction. In this paper we present and illustrate PLSC and PLSR and show how these descriptive multivariate analysis techniques can be extended to deal with inferential questions by using cross-validation techniques such as the bootstrap and permutation tests.
Analysis of a non-standard mixed finite element method with applications to superconvergence
Brandts, J.H.
2009-01-01
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent. Superconve
Meshfree First-order System Least Squares
Institute of Scientific and Technical Information of China (English)
Hugh R.MacMillan; Max D.Gunzburger; John V.Burkardt
2008-01-01
We prove convergence for a meshfree first-order system least squares (FOSLS) partition of unity finite element method (PUFEM). Essentially, by virtue of the partition of unity, local approximation gives rise to global approximation in H(div)∩ H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis-cretization. Preliminary numerical results are provided and remaining challenges are discussed.
A Note on Separable Nonlinear Least Squares Problem
Gharibi, Wajeb
2011-01-01
Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas, especially in Operations Research and Computer Sciences. They are difficult to solve with the infinite-norm metric. In this paper, we give a short note on the separable nonlinear least squares problem, unseparated scheme for NLS, and propose an algorithm for solving mixed linear-nonlinear minimization problem, method of which results in solving a series of least squares separable problems.
Nonlinear Least Squares for Inverse Problems
Chavent, Guy
2009-01-01
Presents an introduction into the least squares resolution of nonlinear inverse problems. This title intends to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, that is, both wellposedness and optimizability
Institute of Scientific and Technical Information of China (English)
陈宁; 于德介; 吕辉; 夏百战
2014-01-01
In order to improve the accuracy of simulation analysis of plate structural-acoustic coupled systems,the finite element-least square point interpolation method (FE-LSPIM)was extended to solve plate structural -acoustic coupled problems and a coupled FE-LSPIM for plate structural-acoustic coupled systems was proposed.With the proposed method,the shape functions of the finite element method and the least square point interpolation were used for local approximation,the element-compatibility of the finite element method and the quadratic polynomial completeness of LSPIM were inherited.Thus,the accuracy of simulation analysis could be improved.Numerical example of a box structural-acoustic coupled model was presented.Its results showed that using FE-LSPIMachieves a higher accuracy,compared with using FEMand smoothed FEMfor simulation of plate structural -acoustic coupled problems.%为提高板结构-声场耦合分析的计算精度，将有限元-最小二乘点插值法（Finite Element-Least Square Point Interpolation Method，FE-LSPIM）推广到板结构-声场耦合问题的分析中，提出了板结构-声场耦合问题分析的 FE-LSPIM/FE-LSPIM方法，推导了 FE-LSPIM/FE-LSPIM分析板结构-声场耦合问题的计算公式。FE-LSPIM/FE-LSPIM方法应用有限元单元形函数和最小二乘点插值法进行局部逼近，继承了有限元法的单元兼容性和最小二乘插值法的二次多项式完备性，提高了计算精度。以一六面体声场-结构耦合模型为研究对象进行分析，结果表明，与板结构-声场耦合问题分析的 FEM/FEM和光滑有限元/有限元（Smoothed Finite Element Method /Finite Element Method，SFEM/FEM）相比，FE-LSPIM/FE-LSPIM在分析板结构-声场耦合问题时具有更高的精度。
Tikhonov Regularization and Total Least Squares
DEFF Research Database (Denmark)
Golub, G. H.; Hansen, Per Christian; O'Leary, D. P.
2000-01-01
formulation involves a least squares problem, can be recast in a total least squares formulation suited for problems in which both the coefficient matrix and the right-hand side are known only approximately. We analyze the regularizing properties of this method and demonstrate by a numerical example that...
Collinearity in Least-Squares Analysis
de Levie, Robert
2012-01-01
How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions…
Application of least-squares spectral element solver methods to incompressible flow problems
Proot, M.M.J.; Gerritsma, M.I.; Nool, M.
2003-01-01
Least-squares spectral element methods are based on two important and successful numerical methods: spectral /hp element methods and least-squares finite element methods. In this respect, least-squares spectral element methods are very powerfull since they combine the generality of finite element me
Institute of Scientific and Technical Information of China (English)
冯德山; 王珣
2013-01-01
Based on the boundary value problem of partial differential equation of the two-dimensional magnetotelluric (MT) forward modeling meet, the detail algorithm of finite element method deduced by the rectangular grid subdivision and cell biquadratic interpolation method were used to solve the electromagnetic problems both in TE and TM polarization mode. By using the basic theory of inversion, the solving ill-posed problem regularization method was applied to the least-square optimization approach, and the most smoothness constrained least square regularization inversion objective function was gotten, then a completed two-dimensional magnetotelluric forward computational program was written by Matlab. This program was applied on high/low resistance geoelectric model and Sasaki model, the inversion cross-sectional profiles of TE mode, TM mode and TE&TM joint inversion model separately were plotted. Compared the inversion results with the original models, TE mode inversion profile has higher vertical resolution, TM mode has higher lateral resolution, TE&TM joint inversion is superior to the single inversion of polarization mode. At the same time, MT biquadratic interpolation finite element forward modeling and least-square regularization inversion algorithm are proved to be effective and feasible.%从大地电磁(MT)二维正演所满足的偏微分方程边值问题出发，应用矩形网格剖分和单元内双二次插值推导有限单元法求解大地电磁TE与TM两种极化模式正问题详细算法。应用反演理论将病态问题求解的正则化方法应用到最小二乘优化方法中，获得最光滑约束最小二乘正则化反演目标函数，并利用Matlab编制了大地电磁二维正反演计算程序。应用该程序对高低阻地电模型和Sasaki模型开展了正反演计算，并绘制TE模式和TM模式、TE&TM联合反演模式的反演成果剖面图。将所得的反演剖面与初始模型对比可知，TE模式反演
Institute of Scientific and Technical Information of China (English)
陈善群; 廖斌; 李海峰
2012-01-01
Meshfree methods could be used to deliberately distribute nodes freely and simply in the computational domain free from constraints. Compared with traditional methods, meshfree methods have greater ability to deal with complex boundary. In this paper, a Meshfree Least-Squares-based Finite Difference (ML5FD) method is applied to the calculation of 2-D non-conservative shallow water equations. Two solutions are presented for nodes selection. In order to avoid cumbersome examination process, the least square technique is introduced to optimize the approximation of the vector. The MLSFD method is employed to simulate a circular dam-break model. To treat boundary condition better, three-layer right-angle grids are distributed from the boundary to the inside around the meshfree nodes. Numerical simulation results are analyzed and compared. The results show that the MLSFD method has a high accuracy of simulating 2-D shallow water flow. It' s indicated that the MLSFD method is feasible for solving shallow water equations.%近年来兴起的无网格方法摆脱了网格约束,在计算区域内能自由布点,快速灵活,并且离散节点能更好地拟合复杂的边界,求解精度较高.运用最小二乘无网格有限差分(MLSFD)方法,求解二维非守恒形式浅水方程.支撑域内点采用2种方法结合的方式进行选取.为避开繁琐的矩阵奇异、病态的检验过程,选用了最小二乘技术对矢量做最优化近似,并使用MLSFD对圆形溃坝模型进行计算.为了更好地处理边界条件,在无网格的四周,向内分别布置三层直角网格.对数值模拟结果进行分析比较,验证了该方法在计算二维浅水流动的数值模拟方面有着较高的精确度,进而说明无网格方法运用于求解浅水方程是可行的.
An Orthogonal Least Squares Based Approach to FIR Designs
Institute of Scientific and Technical Information of China (English)
Xiao-Feng Wu; Zi-Qiang Lang; Stephen A Billings
2005-01-01
This paper is concerned with the application of forward Orthogonal Least Squares (OLS) algorithm to the design of Finite Impulse Response (FIR) filters. The focus of this study is a new FIR filter design procedure and to compare this with traditional methods known as the fir2() routine provided by MATLAB.
Energy Technology Data Exchange (ETDEWEB)
Bloechle, B.; Manteuffel, T.; McCormick, S.; Starke, G.
1996-12-31
Many physical phenomena are modeled as scalar second-order elliptic boundary value problems with discontinuous coefficients. The first-order system least-squares (FOSLS) methodology is an alternative to standard mixed finite element methods for such problems. The occurrence of singularities at interface corners and cross-points requires that care be taken when implementing the least-squares finite element method in the FOSLS context. We introduce two methods of handling the challenges resulting from singularities. The first method is based on a weighted least-squares functional and results in non-conforming finite elements. The second method is based on the use of singular basis functions and results in conforming finite elements. We also share numerical results comparing the two approaches.
Parallel Implementation of a Least-Squares Spectral Element Solver for Incomressible Flow Problems
Nool, M.; Proot, M.M.J.; Sloot, P.M.A.; Kenneth Tan, C.J.; Dongarra, J.J.; Hoekstra, A.G.
2002-01-01
Least-squares spectral element methods are based on two important and successful numerical methods: spectral/{\\em hp} element methods and least-squares finite element methods. Least-squares methods lead to symmetric and positive definite algebraic systems which circumvent the Ladyzhenskaya-Babu\\v{s}
Least Squares Data Fitting with Applications
DEFF Research Database (Denmark)
Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela
predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis......As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data...
Least Squares Data Fitting with Applications
DEFF Research Database (Denmark)
Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data...... predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis...
Partial update least-square adaptive filtering
Xie, Bei
2014-01-01
Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity (O(N)) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster a
Deformation analysis with Total Least Squares
Directory of Open Access Journals (Sweden)
M. Acar
2006-01-01
Full Text Available Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS and the Total Least Squares (TLS, respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.
Combinatorics of least-squares trees.
Mihaescu, Radu; Pachter, Lior
2008-09-01
A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least-squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four-point condition that the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss-Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution, and the taxon-weighted variance model. They also provide a time-optimal algorithm for computation.
Iterative methods for weighted least-squares
Energy Technology Data Exchange (ETDEWEB)
Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.
Least-squares fitting Gompertz curve
Jukic, Dragan; Kralik, Gordana; Scitovski, Rudolf
2004-08-01
In this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,...,m, m≥3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples.
Consistent Partial Least Squares Path Modeling
Dijkstra, Theo K.; Henseler, Jörg
2015-01-01
This paper resumes the discussion in information systems research on the use of partial least squares (PLS) path modeling and shows that the inconsistency of PLS path coefficient estimates in the case of reflective measurement can have adverse consequences for hypothesis testing. To remedy this, the
Time Scale in Least Square Method
Directory of Open Access Journals (Sweden)
Özgür Yeniay
2014-01-01
Full Text Available Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.
An Algorithm to Solve Separable Nonlinear Least Square Problem
Directory of Open Access Journals (Sweden)
Wajeb Gharibi
2013-07-01
Full Text Available Separable Nonlinear Least Squares (SNLS problem is a special class of Nonlinear Least Squares (NLS problems, whose objective function is a mixture of linear and nonlinear functions. SNLS has many applications in several areas, especially in the field of Operations Research and Computer Science. Problems related to the class of NLS are hard to resolve having infinite-norm metric. This paper gives a brief explanation about SNLS problem and offers a Lagrangian based algorithm for solving mixed linear-nonlinear minimization problem
Diagonal loading least squares time delay estimation
Institute of Scientific and Technical Information of China (English)
LI Xuan; YAN Shefeng; MA Xiaochuan
2012-01-01
Least squares （LS） time delay estimation is a classical and effective method. However, the performance is degraded severely in the scenario of low ratio of signal-noise （SNR） due to the instability of matrix inversing. In order to solve the problem, diagonal loading least squares （DL-LS） is proposed by adding a positive definite matrix to the inverse matrix. Furthermore, the shortcoming of fixed diagonal loading is analyzed from the point of regularization that when the tolerance of low SNR is increased, veracity is decreased. This problem is resolved by reloading. The primary estimation＇s reciprocal is introduced as diagonal loading and it leads to small diagonal loading at the time of arrival and larger loading at other time. Simulation and pool experiment prove the algorithm has better performance.
Least Squares Moving-Window Spectral Analysis.
Lee, Young Jong
2017-01-01
Least squares regression is proposed as a moving-windows method for analysis of a series of spectra acquired as a function of external perturbation. The least squares moving-window (LSMW) method can be considered an extended form of the Savitzky-Golay differentiation for nonuniform perturbation spacing. LSMW is characterized in terms of moving-window size, perturbation spacing type, and intensity noise. Simulation results from LSMW are compared with results from other numerical differentiation methods, such as single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods. It is demonstrated that this simple LSMW method can be useful for quantitative analysis of nonuniformly spaced spectral data with high frequency noise.
On derivative estimation and the solution of least squares problems
Belward, John A.; Turner, Ian W.; Ilic, Milos
2008-12-01
Surface interpolation finds application in many aspects of science and technology. Two specific areas of interest are surface reconstruction techniques for plant architecture and approximating cell face fluxes in the finite volume discretisation strategy for solving partial differential equations numerically. An important requirement of both applications is accurate local gradient estimation. In surface reconstruction this gradient information is used to increase the accuracy of the local interpolant, while in the finite volume framework accurate gradient information is essential to ensure second order spatial accuracy of the discretisation. In this work two different least squares strategies for approximating these local gradients are investigated and the errors associated with each analysed. It is shown that although the two strategies appear different, they produce the same least squares error. Some carefully chosen case studies are used to elucidate this finding.
Steady and transient least square solvers for thermal problems
Padovan, Joe
1987-01-01
This paper develops a hierarchical least square solution algorithm for highly nonlinear heat transfer problems. The methodology's capability is such that both steady and transient implicit formulations can be handled. This includes problems arising from highly nonlinear heat transfer systems modeled by either finite-element or finite-difference schemes. The overall procedure developed enables localized updating, iteration, and convergence checking as well as constraint application. The localized updating can be performed at a variety of hierarchical levels, i.e., degree of freedom, substructural, material-nonlinear groups, and/or boundary groups. The choice of such partitions can be made via energy partitioning or nonlinearity levels as well as by user selection. Overall, this leads to extremely robust computational characteristics. To demonstrate the methodology, problems are drawn from nonlinear heat conduction. These are used to quantify the robust capabilities of the hierarchical least square scheme.
An iterative approach to a constrained least squares problem
Directory of Open Access Journals (Sweden)
Simeon Reich
2003-01-01
In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H, an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The net of the solutions to the regularized problems strongly converges to the minimum norm solution of the least squares problem if its solution set is nonempty.
Efficient least-squares basket-weaving
Winkel, B.; Flöer, L.; Kraus, A.
2012-11-01
We report on a novel method to solve the basket-weaving problem. Basket-weaving is a technique that is used to remove scan-line patterns from single-dish radio maps. The new approach applies linear least-squares and works on gridded maps from arbitrarily sampled data, which greatly improves computational efficiency and robustness. It also allows masking of bad data, which is useful for cases where radio frequency interference is present in the data. We evaluate the algorithms using simulations and real data obtained with the Effelsberg 100-m telescope.
Efficient least-squares basket-weaving
Winkel, B; Kraus, A
2012-01-01
We report on a novel method to solve the basket-weaving problem. Basket-weaving is a technique that is used to remove scan-line patterns from single-dish radio maps. The new approach applies linear least-squares and works on gridded maps from arbitrarily sampled data, which greatly improves computational efficiency and robustness. It also allows masking of bad data, which is useful for cases where radio frequency interference is present in the data. We evaluate the algorithms using simulations and real data obtained with the Effelsberg 100-m telescope.
Least-squares Gaussian beam migration
Yuan, Maolin; Huang, Jianping; Liao, Wenyuan; Jiang, Fuyou
2017-02-01
A theory of least-squares Gaussian beam migration (LSGBM) is presented to optimally estimate a subsurface reflectivity. In the iterative inversion scheme, a Gaussian beam (GB) propagator is used as the kernel of linearized forward modeling (demigration) and its adjoint (migration). Born approximation based GB demigration relies on the calculation of Green’s function by a Gaussian-beam summation for the downward and upward wavefields. The adjoint operator of GB demigration accounts for GB prestack depth migration under the cross-correlation imaging condition, where seismic traces are processed one by one for each shot. A numerical test on the point diffractors model suggests that GB demigration can successfully simulate primary scattered data, while migration (adjoint) can yield a corresponding image. The GB demigration/migration algorithms are used for the least-squares migration scheme to deblur conventional migrated images. The proposed LSGBM is illustrated with two synthetic data for a four-layer model and the Marmousi2 model. Numerical results show that LSGBM, compared to migration (adjoint) with GBs, produces images with more balanced amplitude, higher resolution and even fewer artifacts. Additionally, the LSGBM shows a robust convergence rate.
Total least squares for anomalous change detection
Energy Technology Data Exchange (ETDEWEB)
Theiler, James P [Los Alamos National Laboratory; Matsekh, Anna M [Los Alamos National Laboratory
2010-01-01
A family of difference-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQ-based anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and furthermore it is shown to be equivalent to the optimized covariance equalization algorithm. What whitened TLSQ offers, in addition to connecting with a common language the derivations of two of the most popular anomalous change detection algorithms - chronochrome and covariance equalization - is a generalization of these algorithms with the potential for better performance.
Augmented Classical Least Squares Multivariate Spectral Analysis
Energy Technology Data Exchange (ETDEWEB)
Haaland, David M. (Albuquerque, NM); Melgaard, David K. (Albuquerque, NM)
2005-01-11
A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.
Augmented Classical Least Squares Multivariate Spectral Analysis
Energy Technology Data Exchange (ETDEWEB)
Haaland, David M. (Albuquerque, NM); Melgaard, David K. (Albuquerque, NM)
2005-07-26
A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.
Multilevel first-order system least squares for PDEs
Energy Technology Data Exchange (ETDEWEB)
McCormick, S.
1994-12-31
The purpose of this talk is to analyze the least-squares finite element method for second-order convection-diffusion equations written as a first-order system. In general, standard Galerkin finite element methods applied to non-self-adjoint elliptic equations with significant convection terms exhibit a variety of deficiencies, including oscillations or nonmonotonicity of the solution and poor approximation of its derivatives, A variety of stabilization techniques, such as up-winding, Petrov-Galerkin, and stream-line diffusion approximations, have been introduced to eliminate these and other drawbacks of standard Galerkin methods. Yet, although significant progress has been made, convection-diffusion problems remain among the more difficult problems to solve numerically. The first-order system least-squares approach promises to overcome these deficiencies. This talk develops ellipticity estimates and discretization error bounds for elliptic equations (with lower order terms) that are reformulated as a least-squares problem for an equivalent first-order system. The main results are the proofs of ellipticity and optimal convergence of multiplicative and additive solvers of the discrete systems.
NEGATIVE NORM LEAST-SQUARES METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gao Shaoqin; Duan Huoyuan
2008-01-01
The purpose of this article is to develop and analyze least-squares approxi-mations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi (LBB) condition. The authors employ least-squares func-tionals which involve a discrete inner product which is related to the inner product in H-1(Ω).
Multiples least-squares reverse time migration
Zhang, D. L.
2013-01-01
To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated as a virtual source, knowledge of the source wavelet is not required. Numerical tests on synthetic data for the Sigsbee2B model and field data from Gulf of Mexico show that MLSRTM can improve the image quality by removing artifacts, balancing amplitudes, and suppressing crosstalk compared to standard migration of the free-surface multiples. The potential liability of this method is that multiples require several roundtrips between the reflector and the free surface, so that high frequencies in the multiples are attenuated compared to the primary reflections. This can lead to lower resolution in the migration image compared to that computed from primaries.
Least square regularized regression in sum space.
Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu
2013-04-01
This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.
Cichocki, A; Unbehauen, R
1994-01-01
In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.
Multisource Least-squares Reverse Time Migration
Dai, Wei
2012-12-01
Least-squares migration has been shown to be able to produce high quality migration images, but its computational cost is considered to be too high for practical imaging. In this dissertation, a multisource least-squares reverse time migration algorithm (LSRTM) is proposed to increase by up to 10 times the computational efficiency by utilizing the blended sources processing technique. There are three main chapters in this dissertation. In Chapter 2, the multisource LSRTM algorithm is implemented with random time-shift and random source polarity encoding functions. Numerical tests on the 2D HESS VTI data show that the multisource LSRTM algorithm suppresses migration artifacts, balances the amplitudes, improves image resolution, and reduces crosstalk noise associated with the blended shot gathers. For this example, multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution, and fewer migration artifacts compared to conventional RTM. The empirical results suggest that the multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with similar or less computational cost. The caveat is that LSRTM image is sensitive to large errors in the migration velocity model. In Chapter 3, the multisource LSRTM algorithm is implemented with frequency selection encoding strategy and applied to marine streamer data, for which traditional random encoding functions are not applicable. The frequency-selection encoding functions are delta functions in the frequency domain, so that all the encoded shots have unique non-overlapping frequency content. Therefore, the receivers can distinguish the wavefield from each shot according to the frequencies. With the frequency-selection encoding method, the computational efficiency of LSRTM is increased so that its cost is
Elastic least-squares reverse time migration
Feng, Zongcai
2017-03-08
We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.
Skeletonized Least Squares Wave Equation Migration
Zhan, Ge
2010-10-17
The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
Experiments on Coordinate Transformation based on Least Squares and Total Least Squares Methods
Tunalioglu, Nursu; Mustafa Durdag, Utkan; Hasan Dogan, Ali; Erdogan, Bahattin; Ocalan, Taylan
2016-04-01
Coordinate transformation is an important problem in geodesy discipline. Variations in stochastic and functional models in transformation problem cause different estimation results. Least-squares (LS) method is generally implemented to solve this problem. LS method accepts only one epoch coordinate data group erroneous in stochastic model. However, all the data in transformation problem are erroneous. In contrast to the traditional LS method, the Total Least Squares (TLS) method takes into account the errors in all the variables in the transformation. It is so-called errors-invariables (EIV) model. In the last decades, TLS method has been implemented to solve transformation problem. In this context, it is important to determine which method is more accurate. In this study, LS and TLS methods have been implemented on different 2D and 3D geodetic networks with different simulation scenarios. The first results show that the translation parameters are affected more than rotation and scale parameters. Although TLS method considers the errors for two coordinate the estimated parameters for both methods are different from simulated values.
Iterative least-squares solvers for the Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Bochev, P. [Univ. of Texas, Arlington, TX (United States)
1996-12-31
In the recent years finite element methods of least-squares type have attracted considerable attention from both mathematicians and engineers. This interest has been motivated, to a large extent, by several valuable analytic and computational properties of least-squares variational principles. In particular, finite element methods based on such principles circumvent Ladyzhenskaya-Babuska-Brezzi condition and lead to symmetric and positive definite algebraic systems. Thus, it is not surprising that numerical solution of fluid flow problems has been among the most promising and successful applications of least-squares methods. In this context least-squares methods offer significant theoretical and practical advantages in the algorithmic design, which makes resulting methods suitable, among other things, for large-scale numerical simulations.
Simultaneous least squares fitter based on the Langrange multiplier method
Guan, Yinghui; Zheng, Yangheng; Zhu, Yong-Sheng
2013-01-01
We developed a least squares fitter used for extracting expected physics parameters from the correlated experimental data in high energy physics. This fitter considers the correlations among the observables and handles the nonlinearity using linearization during the $\\chi^2$ minimization. This method can naturally be extended to the analysis with external inputs. By incorporating with Langrange multipliers, the fitter includes constraints among the measured observables and the parameters of interest. We applied this fitter to the study of the $D^{0}-\\bar{D}^{0}$ mixing parameters as the test-bed based on MC simulation. The test results show that the fitter gives unbiased estimators with correct uncertainties and the approach is credible.
Least Square Approximation by Linear Combinations of Multi(Poles).
1983-04-01
ID-R134 069 LEAST SQUARE APPROXIMATION BY LINEAR COMBINATIONS OF i/i MULTI(POLES). 1U OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEY...TR-83-0 117 LEAST SQUARE APPROXIMATION BY LINEAR COMBINATIONS OF (MULTI)POLES WILLI FREEDEN DEPARTMENT OF GEODETIC SCIENCE AND SURVEYING THE OHIO...Subtitle) S. TYPE OF REPORT & PERIOD COVERED LEAST SQUARE APPROXIMATION BY LINEAR Scientific Report No. 3 COMBINATIONS OF (MULTI)POLES 6. PERFORMING ORG
The least-square method in complex number domain
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The classical least-square method was extended from the real number into the complex number domain, which is called the complex least-square method. The mathematical derivation and its applications show that the complex least-square method is different from one that the real number and the imaginary number are separately calculated with the classical least-square, by which the actual leastsquare estimation cannot be obtained in practice. Applications of this new method to an arbitrarily given series and to the precipitation in rainy season at 160 meteorological stations in China mainland show advantages of this method over other conventional statistical models.
Neither fixed nor random: weighted least squares meta-regression.
Stanley, T D; Doucouliagos, Hristos
2016-06-20
Our study revisits and challenges two core conventional meta-regression estimators: the prevalent use of 'mixed-effects' or random-effects meta-regression analysis and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why an unrestricted weighted least squares MRA (WLS-MRA) estimator is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias that is as good as FE-MRA in all cases and better than fixed effects in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients that are practically equivalent to mixed effects or random effects when there is no publication bias. When there is publication selection bias, WLS-MRA always has smaller bias than mixed effects or random effects. In practical applications, an unrestricted WLS meta-regression is likely to give practically equivalent or superior estimates to fixed-effects, random-effects, and mixed-effects meta-regression approaches. However, random-effects meta-regression remains viable and perhaps somewhat preferable if selection for statistical significance (publication bias) can be ruled out and when random, additive normal heterogeneity is known to directly affect the 'true' regression coefficient. Copyright © 2016 John Wiley & Sons, Ltd.
Solution of a Complex Least Squares Problem with Constrained Phase.
Bydder, Mark
2010-12-30
The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.
An Algorithm for Positive Definite Least Square Estimation of Parameters.
1986-05-01
This document presents an algorithm for positive definite least square estimation of parameters. This estimation problem arises from the PILOT...dynamic macro-economic model and is equivalent to an infinite convex quadratic program. It differs from ordinary least square estimations in that the
note: The least square nucleolus is a general nucleolus
Elisenda Molina; Juan Tejada
2000-01-01
This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the least square nucleolus is a general nucleolus (Maschler et al. (1992)).
Abnormal behavior of the least squares estimate of multiple regression
Institute of Scientific and Technical Information of China (English)
陈希孺; 安鸿志
1997-01-01
An example is given to reveal the abnormal behavior of the least squares estimate of multiple regression. It is shown that the least squares estimate of the multiple linear regression may be "improved in the sense of weak consistency when nuisance parameters are introduced into the model. A discussion on the implications of this finding is given.
Using Weighted Least Squares Regression for Obtaining Langmuir Sorption Constants
One of the most commonly used models for describing phosphorus (P) sorption to soils is the Langmuir model. To obtain model parameters, the Langmuir model is fit to measured sorption data using least squares regression. Least squares regression is based on several assumptions including normally dist...
Visualizing Least-Square Lines of Best Fit.
Engebretsen, Arne
1997-01-01
Presents strategies that utilize graphing calculators and computer software to help students understand the concept of minimizing the squared residuals to find the line of best fit. Includes directions for least-squares drawings using a variety of technologies. (DDR)
Performance Evaluation of the Ordinary Least Square (OLS) and ...
African Journals Online (AJOL)
Nana Kwasi Peprah
Keywords: Differential Global Positioning, System, Total Least Square, Ordinary ... observation equations where only the observations are considered as ..... Dreiseitl, S., and Ohno-Machado, L. (2002), “Logistic Regression and Artificial Neural.
A Newton Algorithm for Multivariate Total Least Squares Problems
Directory of Open Access Journals (Sweden)
WANG Leyang
2016-04-01
Full Text Available In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.
A novel extended kernel recursive least squares algorithm.
Zhu, Pingping; Chen, Badong; Príncipe, José C
2012-08-01
In this paper, a novel extended kernel recursive least squares algorithm is proposed combining the kernel recursive least squares algorithm and the Kalman filter or its extensions to estimate or predict signals. Unlike the extended kernel recursive least squares (Ex-KRLS) algorithm proposed by Liu, the state model of our algorithm is still constructed in the original state space and the hidden state is estimated using the Kalman filter. The measurement model used in hidden state estimation is learned by the kernel recursive least squares algorithm (KRLS) in reproducing kernel Hilbert space (RKHS). The novel algorithm has more flexible state and noise models. We apply this algorithm to vehicle tracking and the nonlinear Rayleigh fading channel tracking, and compare the tracking performances with other existing algorithms.
Generalized Penalized Least Squares and Its Statistical Characteristics
Institute of Scientific and Technical Information of China (English)
DING Shijun; TAO Benzao
2006-01-01
The solution properties of semiparametric model are analyzed, especially that penalized least squares for semiparametric model will be invalid when the matrix BTPB is ill-posed or singular. According to the principle of ridge estimate for linear parametric model, generalized penalized least squares for semiparametric model are put forward, and some formulae and statistical properties of estimates are derived. Finally according to simulation examples some helpful conclusions are drawn.
An application of least squares fit mapping to clinical classification.
Yang, Y.; Chute, C. G.
1992-01-01
This paper describes a unique approach, "Least Square Fit Mapping," to clinical data classification. We use large collections of human-assigned text-to-category matches as training sets to compute the correlations between physicians' terms and canonical concepts. A Linear Least Squares Fit (LLSF) technique is employed to obtain a mapping function which optimally fits the known matches given in a training set and probabilistically captures the unknown matches for arbitrary texts. We tested our...
Recursive least squares background prediction of univariate syndromic surveillance data
Burkom Howard; Najmi Amir-Homayoon
2009-01-01
Abstract Background Surveillance of univariate syndromic data as a means of potential indicator of developing public health conditions has been used extensively. This paper aims to improve the performance of detecting outbreaks by using a background forecasting algorithm based on the adaptive recursive least squares method combined with a novel treatment of the Day of the Week effect. Methods Previous work by the first author has suggested that univariate recursive least squares analysis of s...
A Generalized Autocovariance Least-Squares Method for Covariance Estimation
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad;
2007-01-01
A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter.......A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter....
Least-squares reverse time migration in elastic media
Ren, Zhiming; Liu, Yang; Sen, Mrinal K.
2017-02-01
Elastic reverse time migration (RTM) can yield accurate subsurface information (e.g. PP and PS reflectivity) by imaging the multicomponent seismic data. However, the existing RTM methods are still insufficient to provide satisfactory results because of the finite recording aperture, limited bandwidth and imperfect illumination. Besides, the P- and S-wave separation and the polarity reversal correction are indispensable in conventional elastic RTM. Here, we propose an iterative elastic least-squares RTM (LSRTM) method, in which the imaging accuracy is improved gradually with iteration. We first use the Born approximation to formulate the elastic de-migration operator, and employ the Lagrange multiplier method to derive the adjoint equations and gradients with respect to reflectivity. Then, an efficient inversion workflow (only four forward computations needed in each iteration) is introduced to update the reflectivity. Synthetic and field data examples reveal that the proposed LSRTM method can obtain higher-quality images than the conventional elastic RTM. We also analyse the influence of model parametrizations and misfit functions in elastic LSRTM. We observe that Lamé parameters, velocity and impedance parametrizations have similar and plausible migration results when the structures of different models are correlated. For an uncorrelated subsurface model, velocity and impedance parametrizations produce fewer artefacts caused by parameter crosstalk than the Lamé coefficient parametrization. Correlation- and convolution-type misfit functions are effective when amplitude errors are involved and the source wavelet is unknown, respectively. Finally, we discuss the dependence of elastic LSRTM on migration velocities and its antinoise ability. Imaging results determine that the new elastic LSRTM method performs well as long as the low-frequency components of migration velocities are correct. The quality of images of elastic LSRTM degrades with increasing noise.
Adjoint sensitivity in PDE constrained least squares problems as a multiphysics problem
Lahaye, D.; Mulckhuyse, W.F.W.
2012-01-01
Purpose - The purpose of this paper is to provide a framework for the implementation of an adjoint sensitivity formulation for least-squares partial differential equations constrained optimization problems exploiting a multiphysics finite elements package. The estimation of the diffusion coefficient
Performance analysis of the Least-Squares estimator in Astrometry
Lobos, Rodrigo A; Mendez, Rene A; Orchard, Marcos
2015-01-01
We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not offer a closed-form expression, but a new result is presented (Theorem 1) where both the bias and the mean-square-error of the least-squares estimator are bounded and approximated analytically, in the latter case in terms of a nominal value and an interval around it. From the predicted nominal value we analyze how efficient is the least-squares estimator in comparison with the minimum variance Cramer-Rao bound. Based on our results, we show that, for the high signal-to-noise ratio regime, the performance of the least-squares estimator is significantly poorer than the Cramer-Rao bound, and we characterize this gap analytically. On the positive side, we show that for the challenging low signal-to-noise regime (attributed to either a weak astronomical signal or a noise-dominated...
Padovan, J.; Lackney, J.
1986-01-01
The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.
Distributed Recursive Least-Squares: Stability and Performance Analysis
Mateos, Gonzalo
2011-01-01
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying...
Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)
Ni, Angxiu
2016-01-01
This paper develops the tangent Non-Intrusive Least Square Shadowing (NILSS) method, which computes sensitivity for chaotic dynamical systems. In NILSS, a tangent solution is represented as a linear combination of a inhomogeneous tangent solution and some homogeneous tangent solutions. Then we solve a least square problem under this new representation. As a result, this new variant is easier to implement with existing solvers. For chaotic systems with large degrees of freedom but low dimensional attractors, NILSS has low computation cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system, and a CFD simulation of a backward-facing step. The results show that NILSS computes the correct derivative with a lower cost than the conventional Least Square Shadowing method and the conventional finite difference method.
Institute of Scientific and Technical Information of China (English)
孙孝前; 尤进红
2003-01-01
In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal. An iterative weighted partial spline least squares estimator (IWPSLSE) for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE) with weights constructed by using the within-group partial spline least squares residuals in the senseof asymptotic variance. The asymptotic normality of this IWPSLSE is established. An adaptive procedure ispresented which ensures that the iterative process stops after a finite number of iterations and produces anestimator asymptotically equivalent to the best estimator that can be obtained by using the iterative proce-dure. These results are generalizations of those in heteroscedastic linear model to the case of semiparametric regression.
A note on the limitations of lattice least squares
Gillis, J. T.; Gustafson, C. L.; Mcgraw, G. A.
1988-01-01
This paper quantifies the known limitation of lattice least squares to ARX models in terms of the dynamic properties of the system being modeled. This allows determination of the applicability of lattice least squares in a given situation. The central result is that an equivalent ARX model exists for an ARMAX system if and only if the ARMAX system has no transmission zeros from the noise port to the output port. The technique used to prove this fact is a construction using the matrix fractional description of the system. The final section presents two computational examples.
Multi-source least-squares migration of marine data
Wang, Xin
2012-11-04
Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes) is applied to the receiver side traces. Results show that the MSLSM images are of better quality than the standard Kirchhoff migration and reverse time migration images; moreover, the migration artifacts are reduced and image resolution is significantly improved. The computational cost of MSLSM is about the same as conventional least-squares migration, but its IO cost is significantly decreased.
Sparse least-squares reverse time migration using seislets
Dutta, Gaurav
2015-08-19
We propose sparse least-squares reverse time migration (LSRTM) using seislets as a basis for the reflectivity distribution. This basis is used along with a dip-constrained preconditioner that emphasizes image updates only along prominent dips during the iterations. These dips can be estimated from the standard migration image or from the gradient using plane-wave destruction filters or structural tensors. Numerical tests on synthetic datasets demonstrate the benefits of this method for mitigation of aliasing artifacts and crosstalk noise in multisource least-squares migration.
HERMITE SCATTERED DATA FITTING BY THE PENALIZED LEAST SQUARES METHOD
Institute of Scientific and Technical Information of China (English)
Tianhe Zhou; Danfu Han
2009-01-01
Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker[Serdica, 18 (2002), pp.1001-1020]to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bound for the extension method. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.
Least-squares variance component estimation: theory and GPS applications
Amiri-Simkooei, A.
2007-01-01
In this thesis we study the method of least-squares variance component estimation (LS-VCE) and elaborate on theoretical and practical aspects of the method. We show that LS-VCE is a simple, flexible, and attractive VCE-method. The LS-VCE method is simple because it is based on the well-known principle of least-squares. With this method the estimation of the (co)variance components is based on a linear model of observation equations. The method is flexible since it works with a user-defined we...
Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function
Seijo, Emilio
2010-01-01
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided. We also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization, computation and consistency of its least squares estimator.
Institute of Scientific and Technical Information of China (English)
Xin LIU; Guo WEI; Jin-wei SUN; Dan LIU
2009-01-01
Least squares support vector machines (LS-SVMs) are modified support vector machines (SVMs) that involve equality constraints and work with a least squares cost function, which simplifies the optimization procedure. In this paper, a novel training algorithm based on total least squares (TLS) for an LS-SVM is presented and applied to muhifunctional sensor signal reconstruction. For three different nonlinearities of a multi functional sensor model, the reconstruction accuracies of input signals are 0.001 36%, 0.03184% and 0.504 80%, respectively. The experimental results demonstrate the higher reliability and accuracy of the proposed method for multi functional sensor signal reconstruction than the original LS-SVM training algorithm, and verify the feasibility and stability of the proposed method.
A Hybrid Method for Nonlinear Least Squares Problems
Institute of Scientific and Technical Information of China (English)
Zhongyi Liu; Linping Sun
2007-01-01
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method,a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual,small-residual and large-residual problems.
Consistency of System Identification by Global Total Least Squares
C. Heij (Christiaan); W. Scherrer
1996-01-01
textabstractGlobal total least squares (GTLS) is a method for the identification of linear systems where no distinction between input and output variables is required. This method has been developed within the deterministic behavioural approach to systems. In this paper we analyse statistical proper
Consistency of global total least squares in stochastic system identification
C. Heij (Christiaan); W. Scherrer
1995-01-01
textabstractGlobal total least squares has been introduced as a method for the identification of deterministic system behaviours. We analyse this method within a stochastic framework, where the observed data are generated by a stationary stochastic process. Conditions are formulated so that the meth
Integer least-squares theory for the GNSS compass
Teunissen, P.J.G.
2010-01-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategi
Risk and Management Control: A Partial Least Square Modelling Approach
DEFF Research Database (Denmark)
Nielsen, Steen; Pontoppidan, Iens Christian
and interrelations between risk and areas within management accounting. The idea is that management accounting should be able to conduct a valid feed forward but also predictions for decision making including risk. This study reports the test of a theoretical model using partial least squares (PLS) on survey data...
A Genetic Algorithm Approach to Nonlinear Least Squares Estimation
Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.
2004-01-01
A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…
SELECTION OF REFERENCE PLANE BY THE LEAST SQUARES FITTING METHODS
Directory of Open Access Journals (Sweden)
Przemysław Podulka
2016-06-01
For least squares polynomial fittings it was found that applied method for cylinder liners gave usually better robustness for scratches, valleys and dimples occurrence. For piston skirt surfaces better edge-filtering results were obtained. It was also recommended to analyse the Sk parameters for proper selection of reference plane in surface topography measurements.
Fuzzy modeling of friction by bacterial and least square optimization
Jastrzebski, Marcin
2006-03-01
In this paper a new method of tuning parameters of Sugeno fuzzy models is presented. Because modeled phenomenon is discontinuous, new type of consequent function was introduced. Described algorithm (BA+LSQ) combines bacterial algorithm (BA) for tuning parameters of membership functions and least square method (LSQ) for parameters of consequent functions.
Plane-wave Least-squares Reverse Time Migration
Dai, Wei
2012-11-04
Least-squares reverse time migration is formulated with a new parameterization, where the migration image of each shot is updated separately and a prestack image is produced with common image gathers. The advantage is that it can offer stable convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A regularization term which penalizes the image difference between nearby angles are used to keep the prestack image consistent through all the angles. Numerical tests on a marine dataset is performed to illustrate the advantages of least-squares reverse time migration in the plane-wave domain. Through iterations of least-squares migration, the migration artifacts are reduced and the image resolution is improved. Empirical results suggest that the LSRTM in plane wave domain is an efficient method to improve the image quality and produce common image gathers.
A least squares estimation method for the linear learning model
B. Wierenga (Berend)
1978-01-01
textabstractThe author presents a new method for estimating the parameters of the linear learning model. The procedure, essentially a least squares method, is easy to carry out and avoids certain difficulties of earlier estimation procedures. Applications to three different data sets are reported, a
Weighted least squares stationary approximations to linear systems.
Bierman, G. J.
1972-01-01
Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.
ON A FAMILY OF MULTIVARIATE LEAST-SQUARES ORTHOGONAL POLYNOMIALS
Institute of Scientific and Technical Information of China (English)
郑成德; 王仁宏
2003-01-01
In this paper the new notion of multivariate least-squares orthogonal poly-nomials from the rectangular form is introduced. Their existence and uniqueness isstudied and some methods for their recursive computation are given. As an applica-is constructed.
On the Routh approximation technique and least squares errors
Aburdene, M. F.; Singh, R.-N. P.
1979-01-01
A new method for calculating the coefficients of the numerator polynomial of the direct Routh approximation method (DRAM) using the least square error criterion is formulated. The necessary conditions have been obtained in terms of algebraic equations. The method is useful for low frequency as well as high frequency reduced-order models.
Optimization of sequential decisions by least squares Monte Carlo method
DEFF Research Database (Denmark)
Nishijima, Kazuyoshi; Anders, Annett
change adaptation measures, and evacuation of people and assets in the face of an emerging natural hazard event. Focusing on the last example, an efficient solution scheme is proposed by Anders and Nishijima (2011). The proposed solution scheme takes basis in the least squares Monte Carlo method, which...
Least-squares variance component estimation: theory and GPS applications
Amiri-Simkooei, A.
2007-01-01
In this thesis we study the method of least-squares variance component estimation (LS-VCE) and elaborate on theoretical and practical aspects of the method. We show that LS-VCE is a simple, flexible, and attractive VCE-method. The LS-VCE method is simple because it is based on the well-known
Integer least-squares theory for the GNSS compass
Teunissen, P.J.G.
2010-01-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search
Algorithms for unweighted least-squares factor analysis
Krijnen, WP
Estimation of the factor model by unweighted least squares (ULS) is distribution free, yields consistent estimates, and is computationally fast if the Minimum Residuals (MinRes) algorithm is employed, MinRes algorithms produce a converging sequence of monotonically decreasing ULS function values.
ON THE COMPARISION OF THE TOTAL LEAST SQUARES AND THE LEAST SQUARES PROBLEMS%TLS和LS问题的比较
Institute of Scientific and Technical Information of China (English)
刘永辉; 魏木生
2003-01-01
There are a number of articles discussing the total least squares(TLS) and the least squares(LS) problems.M.Wei(M.Wei, Mathematica Numerica Sinica 20(3)(1998),267-278) proposed a new orthogonal projection method to improve existing perturbation bounds of the TLS and LS problems.In this paper,wecontinue to improve existing bounds of differences between the squared residuals,the weighted squared residuals and the minimum norm correction matrices of the TLS and LS problems.
Wave-equation Q tomography and least-squares migration
Dutta, Gaurav
2016-03-01
This thesis designs new methods for Q tomography and Q-compensated prestack depth migration when the recorded seismic data suffer from strong attenuation. A motivation of this work is that the presence of gas clouds or mud channels in overburden structures leads to the distortion of amplitudes and phases in seismic waves propagating inside the earth. If the attenuation parameter Q is very strong, i.e., Q<30, ignoring the anelastic effects in imaging can lead to dimming of migration amplitudes and loss of resolution. This, in turn, adversely affects the ability to accurately predict reservoir properties below such layers. To mitigate this problem, I first develop an anelastic least-squares reverse time migration (Q-LSRTM) technique. I reformulate the conventional acoustic least-squares migration problem as a viscoacoustic linearized inversion problem. Using linearized viscoacoustic modeling and adjoint operators during the least-squares iterations, I show with numerical tests that Q-LSRTM can compensate for the amplitude loss and produce images with better balanced amplitudes than conventional migration. To estimate the background Q model that can be used for any Q-compensating migration algorithm, I then develop a wave-equation based optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through numerical tests on synthetic and field data, I show that noticeable improvements in the migration image quality can be obtained from Q models inverted using wave-equation Q tomography. A key feature of skeletonized inversion is that it is much less likely to get stuck in a local minimum than a standard waveform inversion method. Finally, I develop a preconditioning technique for least-squares migration using a directional Gabor-based preconditioning approach for isotropic
Moving least-squares corrections for smoothed particle hydrodynamics
Directory of Open Access Journals (Sweden)
Ciro Del Negro
2011-12-01
Full Text Available First-order moving least-squares are typically used in conjunction with smoothed particle hydrodynamics in the form of post-processing filters for density fields, to smooth out noise that develops in most applications of smoothed particle hydrodynamics. We show how an approach based on higher-order moving least-squares can be used to correct some of the main limitations in gradient and second-order derivative computation in classic smoothed particle hydrodynamics formulations. With a small increase in computational cost, we manage to achieve smooth density distributions without the need for post-processing and with higher accuracy in the computation of the viscous term of the Navier–Stokes equations, thereby reducing the formation of spurious shockwaves or other streaming effects in the evolution of fluid flow. Numerical tests on a classic two-dimensional dam-break problem confirm the improvement of the new approach.
Least Squares Shadowing for Sensitivity Analysis of Turbulent Fluid Flows
Blonigan, Patrick; Wang, Qiqi
2014-01-01
Computational methods for sensitivity analysis are invaluable tools for aerodynamics research and engineering design. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in turbulent fluid flow fields, specifically those obtained using high-fidelity turbulence simulations. This is because of a number of dynamical properties of turbulent and chaotic fluid flows, most importantly high sensitivity of the initial value problem, popularly known as the "butterfly effect". The recently developed least squares shadowing (LSS) method avoids the issues encountered by traditional sensitivity analysis methods by approximating the "shadow trajectory" in phase space, avoiding the high sensitivity of the initial value problem. The following paper discusses how the least squares problem associated with LSS is solved. Two methods are presented and are demonstrated on a simulation of homogeneous isotropic turbulence and the Kuramoto-Sivashinsky (KS) equation, a 4th order c...
A unified approach for least-squares surface fitting
Institute of Scientific and Technical Information of China (English)
ZHU; Limin; DING; Han
2004-01-01
This paper presents a novel approach for least-squares fitting of complex surface to measured 3D coordinate points by adjusting its location and/or shape. For a point expressed in the machine reference frame and a deformable smooth surface represented in its own model frame, a signed point-to-surface distance function is defined,and its increment with respect to the differential motion and differential deformation of the surface is derived. On this basis, localization, surface reconstruction and geometric variation characterization are formulated as a unified nonlinear least-squares problem defined on the product space SE(3)×m. By using Levenberg-Marquardt method, a sequential approximation surface fitting algorithm is developed. It has the advantages of implementational simplicity, computational efficiency and robustness. Applications confirm the validity of the proposed approach.
Anisotropy minimization via least squares method for transformation optics.
Junqueira, Mateus A F C; Gabrielli, Lucas H; Spadoti, Danilo H
2014-07-28
In this work the least squares method is used to reduce anisotropy in transformation optics technique. To apply the least squares method a power series is added on the coordinate transformation functions. The series coefficients were calculated to reduce the deviations in Cauchy-Riemann equations, which, when satisfied, result in both conformal transformations and isotropic media. We also present a mathematical treatment for the special case of transformation optics to design waveguides. To demonstrate the proposed technique a waveguide with a 30° of bend and with a 50% of increase in its output width was designed. The results show that our technique is simultaneously straightforward to be implement and effective in reducing the anisotropy of the transformation for an extremely low value close to zero.
Linearized least-square imaging of internally scattered data
Aldawood, Ali
2014-01-01
Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single-scattering energy such as nearly vertical faults. Standard migration of these multiples provide subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. Hence, we apply a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. Application to synthetic data demonstrated the effectiveness of the proposed inversion in imaging a reflector that is poorly illuminated by single-scattering energy. The least-square inversion of doublescattered data helped delineate that reflector with minimal acquisition fingerprint.
CONDITION NUMBER FOR WEIGHTED LINEAR LEAST SQUARES PROBLEM
Institute of Scientific and Technical Information of China (English)
Yimin Wei; Huaian Diao; Sanzheng Qiao
2007-01-01
In this paper,we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem:minx ||Ax-b||2,where A is an m-by-n (m≥n)rank deficient matrix.We first derive an explicit expression for the condition number in the weighted Frobenius norm || [AT,βb]||F of the data A and b,where T is a positive diagonal matrix and β is a positive scalar.We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.
Source allocation by least-squares hydrocarbon fingerprint matching
Energy Technology Data Exchange (ETDEWEB)
William A. Burns; Stephen M. Mudge; A. Edward Bence; Paul D. Boehm; John S. Brown; David S. Page; Keith R. Parker [W.A. Burns Consulting Services LLC, Houston, TX (United States)
2006-11-01
There has been much controversy regarding the origins of the natural polycyclic aromatic hydrocarbon (PAH) and chemical biomarker background in Prince William Sound (PWS), Alaska, site of the 1989 Exxon Valdez oil spill. Different authors have attributed the sources to various proportions of coal, natural seep oil, shales, and stream sediments. The different probable bioavailabilities of hydrocarbons from these various sources can affect environmental damage assessments from the spill. This study compares two different approaches to source apportionment with the same data (136 PAHs and biomarkers) and investigate whether increasing the number of coal source samples from one to six increases coal attributions. The constrained least-squares (CLS) source allocation method that fits concentrations meets geologic and chemical constraints better than partial least-squares (PLS) which predicts variance. The field data set was expanded to include coal samples reported by others, and CLS fits confirm earlier findings of low coal contributions to PWS. 15 refs., 5 figs.
SUBSPACE SEARCH METHOD FOR A CLASS OF LEAST SQUARES PROBLEM
Institute of Scientific and Technical Information of China (English)
Zi-Luan Wei
2000-01-01
A subspace search method for solving a class of least squares problem is pre sented in the paper. The original problem is divided into many independent sub problems, and a search direction is obtained by solving each of the subproblems, as well as a new iterative point is determined by choosing a suitable steplength such that the value of residual norm is decreasing. The convergence result is also given. The numerical test is also shown for a special problem,
Parallel Nonnegative Least Squares Solvers for Model Order Reduction
2016-03-01
not for the PQN method. For the latter method the size of the active set is controlled to promote sparse solutions. This is described in Section 3.2.1...or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington...21005-5066 primary author’s email: <james.p.collins106.civ@mail.mil>. Parallel nonnegative least squares (NNLS) solvers are developed specifically for
Kernel Partial Least Squares for Nonlinear Regression and Discrimination
Rosipal, Roman; Clancy, Daniel (Technical Monitor)
2002-01-01
This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.
Least-Square Prediction for Backward Adaptive Video Coding
2006-01-01
Almost all existing approaches towards video coding exploit the temporal redundancy by block-matching-based motion estimation and compensation. Regardless of its popularity, block matching still reflects an ad hoc understanding of the relationship between motion and intensity uncertainty models. In this paper, we present a novel backward adaptive approach, named "least-square prediction" (LSP), and demonstrate its potential in video coding. Motivated by the duality between edge contour in im...
Online least-squares policy iteration for reinforcement learning control
2010-01-01
Reinforcement learning is a promising paradigm for learning optimal control. We consider policy iteration (PI) algorithms for reinforcement learning, which iteratively evaluate and improve control policies. State-of-the-art, least-squares techniques for policy evaluation are sample-efficient and have relaxed convergence requirements. However, they are typically used in offline PI, whereas a central goal of reinforcement learning is to develop online algorithms. Therefore, we propose an online...
MODIFIED LEAST SQUARE METHOD ON COMPUTING DIRICHLET PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the metho...
Penalized Weighted Least Squares for Outlier Detection and Robust Regression
Gao, Xiaoli; Fang, Yixin
2016-01-01
To conduct regression analysis for data contaminated with outliers, many approaches have been proposed for simultaneous outlier detection and robust regression, so is the approach proposed in this manuscript. This new approach is called "penalized weighted least squares" (PWLS). By assigning each observation an individual weight and incorporating a lasso-type penalty on the log-transformation of the weight vector, the PWLS is able to perform outlier detection and robust regression simultaneou...
Least Squares Polynomial Chaos Expansion: A Review of Sampling Strategies
Hadigol, Mohammad; Doostan, Alireza
2017-01-01
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling ...
Multisplitting for linear, least squares and nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
AN ASSESSMENT OF THE MESHLESS WEIGHTED LEAST-SQUARE METHOD
Institute of Scientific and Technical Information of China (English)
PanXiaofei; SzeKimYim; ZhangXiong
2004-01-01
The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high efficiency. Moreover, the coefficient matrix obtained is symmetric and semipositive definite. In this paper, the method is further examined critically. The effects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an infinite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more efficient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equilibrium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.
Multi-source least-squares reverse time migration
Dai, Wei
2012-06-15
Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.
Simple procedures for imposing constraints for nonlinear least squares optimization
Energy Technology Data Exchange (ETDEWEB)
Carvalho, R. [Petrobras, Rio de Janeiro (Brazil); Thompson, L.G.; Redner, R.; Reynolds, A.C. [Univ. of Tulsa, OK (United States)
1995-12-31
Nonlinear regression method (least squares, least absolute value, etc.) have gained acceptance as practical technology for analyzing well-test pressure data. Even for relatively simple problems, however, commonly used algorithms sometimes converge to nonfeasible parameter estimates (e.g., negative permeabilities) resulting in a failure of the method. The primary objective of this work is to present a new method for imaging the objective function across all boundaries imposed to satisfy physical constraints on the parameters. The algorithm is extremely simple and reliable. The method uses an equivalent unconstrained objective function to impose the physical constraints required in the original problem. Thus, it can be used with standard unconstrained least squares software without reprogramming and provides a viable alternative to penalty functions for imposing constraints when estimating well and reservoir parameters from pressure transient data. In this work, the authors also present two methods of implementing the penalty function approach for imposing parameter constraints in a general unconstrained least squares algorithm. Based on their experience, the new imaging method always converges to a feasible solution in less time than the penalty function methods.
Solving linear inequalities in a least squares sense
Energy Technology Data Exchange (ETDEWEB)
Bramley, R.; Winnicka, B. [Indiana Univ., Bloomington, IN (United States)
1994-12-31
Let A {element_of} {Re}{sup mxn} be an arbitrary real matrix, and let b {element_of} {Re}{sup m} a given vector. A familiar problem in computational linear algebra is to solve the system Ax = b in a least squares sense; that is, to find an x* minimizing {parallel}Ax {minus} b{parallel}, where {parallel} {center_dot} {parallel} refers to the vector two-norm. Such an x* solves the normal equations A{sup T}(Ax {minus} b) = 0, and the optimal residual r* = b {minus} Ax* is unique (although x* need not be). The least squares problem is usually interpreted as corresponding to multiple observations, represented by the rows of A and b, on a vector of data x. The observations may be inconsistent, and in this case a solution is sought that minimizes the norm of the residuals. A less familiar problem to numerical linear algebraists is the solution of systems of linear inequalities Ax {le} b in a least squares sense, but the motivation is similar: if a set of observations places upper or lower bounds on linear combinations of variables, the authors want to find x* minimizing {parallel} (Ax {minus} b){sub +} {parallel}, where the i{sup th} component of the vector v{sub +} is the maximum of zero and the i{sup th} component of v.
LEAST-SQUARES SOLUTION OF AXB = D OVER SYMMETRIC POSITIVE SEMIDEFINITE MATRICES X
Institute of Scientific and Technical Information of China (English)
Anping Liao; Zhongzhi Bai
2003-01-01
Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition,we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.
Kernel-based least squares policy iteration for reinforcement learning.
Xu, Xin; Hu, Dewen; Lu, Xicheng
2007-07-01
In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating
Directory of Open Access Journals (Sweden)
Maria Eugênia Zerlotti Mercadante
2003-10-01
Full Text Available Registros do peso à seleção de bovinos Nelore pertencentes aos rebanhos experimentais da Estação Experimental de Zootecnia de Sertãozinho, foram usados para estudar o acréscimo de informações no acesso à estimativa da mudança genética anual, utilizando métodos de quadrados mínimos e de modelo misto. A mudança genética nos três rebanhos (controle-NeC, e selecionados-NeS e NeT ou somente nos selecionados (NeS e NeT foi estimada, só para fêmeas, por quadrados mínimos, por modelo misto considerando somente o desempenho das fêmeas e incorporando a matriz de parentesco, e por modelo misto incorporando todas as informações disponíveis (registros de machos e fêmeas e matriz de parentesco. A incorporação de todas as informações disponíveis em modelo misto para estimar a mudança genética ao longo dos anos forneceu uma curva mais suavizada das médias anuais e, consequentemente, uma estimativa da tendência genética anual com menor erro-padrão. O método dos quadrados mínimos forneceu estimativas da mudança genética ao longo dos anos altamente variáveis, evidenciando a menor capacidade de particionar a mudança genética da mudança ambiental. O modelo misto incorporando parte das informações de desempenho forneceu estimativas da tendência genética anual muito baixas (viesadas, evidenciando o confundimento da mudança ambiental com o restante da mudança genética não estimada pela ausência de informações.Records of body weight at selection of Nelore cattle pertaining to the Sertãozinho's Experimental Station (SP-Brasil Nelore herds were used to study the influence of the incorporation of additional information on the estimation of annual genetic trend by least squares and mixed model methodologies. The genetic changes in all three Nelore herds (control-NeC and selected-NeS and NeT or only in the selected ones (NeS and NeT were estimated, only for the females, by least squares, by mixed model including their
Image denoising using least squares wavelet support vector machines
Institute of Scientific and Technical Information of China (English)
Guoping Zeng; Ruizhen Zhao
2007-01-01
We propose a new method for image denoising combining wavelet transform and support vector machines (SVMs). A new image filter operator based on the least squares wavelet support vector machines (LSWSVMs) is presented. Noisy image can be denoised through this filter operator and wavelet thresholding technique. Experimental results show that the proposed method is better than the existing SVM regression with the Gaussian radial basis function (RBF) and polynomial RBF. Meanwhile, it can achieve better performance than other traditional methods such as the average filter and median filter.
Spectral feature matching based on partial least squares
Institute of Scientific and Technical Information of China (English)
Weidong Yan; Zheng Tian; Lulu Pan; Mingtao Ding
2009-01-01
We investigate the spectral approaches to the problem of point pattern matching, and present a spectral feature descriptors based on partial least square (PLS). Given keypoints of two images, we define the position similarity matrices respectively, and extract the spectral features from the matrices by PLS, which indicate geometric distribution and inner relationships of the keypoints. Then the keypoints matching is done by bipartite graph matching. The experiments on both synthetic and real-world data corroborate the robustness and invariance of the algorithm.
Positive Scattering Cross Sections using Constrained Least Squares
Energy Technology Data Exchange (ETDEWEB)
Dahl, J.A.; Ganapol, B.D.; Morel, J.E.
1999-09-27
A method which creates a positive Legendre expansion from truncated Legendre cross section libraries is presented. The cross section moments of order two and greater are modified by a constrained least squares algorithm, subject to the constraints that the zeroth and first moments remain constant, and that the standard discrete ordinate scattering matrix is positive. A method using the maximum entropy representation of the cross section which reduces the error of these modified moments is also presented. These methods are implemented in PARTISN, and numerical results from a transport calculation using highly anisotropic scattering cross sections with the exponential discontinuous spatial scheme is presented.
MULTI-RESOLUTION LEAST SQUARES SUPPORT VECTOR MACHINES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The Least Squares Support Vector Machines (LS-SVM) is an improvement to the SVM.Combined the LS-SVM with the Multi-Resolution Analysis (MRA), this letter proposes the Multi-resolution LS-SVM (MLS-SVM). The proposed algorithm has the same theoretical framework as MRA but with better approximation ability. At a fixed scale MLS-SVM is a classical LS-SVM, but MLS-SVM can gradually approximate the target function at different scales. In experiments, the MLS-SVM is used for nonlinear system identification, and achieves better identification accuracy.
Least Squares Adjustment: Linear and Nonlinear Weighted Regression Analysis
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2007-01-01
This note primarily describes the mathematics of least squares regression analysis as it is often used in geodesy including land surveying and satellite positioning applications. In these fields regression is often termed adjustment. The note also contains a couple of typical land surveying...... and satellite positioning application examples. In these application areas we are typically interested in the parameters in the model typically 2- or 3-D positions and not in predictive modelling which is often the main concern in other regression analysis applications. Adjustment is often used to obtain...
Least square estimation of phase, frequency and PDEV
Danielson, Magnus; Rubiola, Enrico
2016-01-01
The Omega-preprocessing was introduced to improve phase noise rejection by using a least square algorithm. The associated variance is the PVAR which is more efficient than MVAR to separate the different noise types. However, unlike AVAR and MVAR, the decimation of PVAR estimates for multi-tau analysis is not possible if each counter measurement is a single scalar. This paper gives a decimation rule based on two scalars, the processing blocks, for each measurement. For the Omega-preprocessing, this implies the definition of an output standard as well as hardware requirements for performing high-speed computations of the blocks.
Classification using least squares support vector machine for reliability analysis
Institute of Scientific and Technical Information of China (English)
Zhi-wei GUO; Guang-chen BAI
2009-01-01
In order to improve the efficiency of the support vector machine (SVM) for classification to deal with a large amount of samples,the least squares support vector machine (LSSVM) for classification methods is introduced into the reliability analysis.To reduce the computational cost,the solution of the SVM is transformed from a quadratic programming to a group of linear equations.The numerical results indicate that the reliability method based on the LSSVM for classification has higher accuracy and requires less computational cost than the SVM method.
Handbook of Partial Least Squares Concepts, Methods and Applications
Vinzi, Vincenzo Esposito; Henseler, Jörg
2010-01-01
This handbook provides a comprehensive overview of Partial Least Squares (PLS) methods with specific reference to their use in marketing and with a discussion of the directions of current research and perspectives. It covers the broad area of PLS methods, from regression to structural equation modeling applications, software and interpretation of results. The handbook serves both as an introduction for those without prior knowledge of PLS and as a comprehensive reference for researchers and practitioners interested in the most recent advances in PLS methodology.
Neural Network Inverse Adaptive Controller Based on Davidon Least Square
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
General neural network inverse adaptive controller haa two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system.These defects limit the scope in which the neural network inverse adaptive controller is used.We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence,and then through constructing the pseudo-plant,a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system.The simulation results show the validity of this scheme.
On the stability and accuracy of least squares approximations
Cohen, Albert; Leviatan, Dany
2011-01-01
We consider the problem of reconstructing an unknown function $f$ on a domain $X$ from samples of $f$ at $n$ randomly chosen points with respect to a given measure $\\rho_X$. Given a sequence of linear spaces $(V_m)_{m>0}$ with ${\\rm dim}(V_m)=m\\leq n$, we study the least squares approximations from the spaces $V_m$. It is well known that such approximations can be inaccurate when $m$ is too close to $n$, even when the samples are noiseless. Our main result provides a criterion on $m$ that describes the needed amount of regularization to ensure that the least squares method is stable and that its accuracy, measured in $L^2(X,\\rho_X)$, is comparable to the best approximation error of $f$ by elements from $V_m$. We illustrate this criterion for various approximation schemes, such as trigonometric polynomials, with $\\rho_X$ being the uniform measure, and algebraic polynomials, with $\\rho_X$ being either the uniform or Chebyshev measure. For such examples we also prove similar stability results using deterministic...
Orthogonal least squares learning algorithm for radial basis function networks
Energy Technology Data Exchange (ETDEWEB)
Chen, S.; Cowan, C.F.N.; Grant, P.M. (Dept. of Electrical Engineering, Univ. of Edinburgh, Mayfield Road, Edinburgh EH9 3JL, Scotland (GB))
1991-03-01
The radial basis function network offers a viable alternative to the two-layer neural network in many applications of signal processing. A common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network. Such a procedure has several drawbacks and, in particular, an arbitrary selection of centers is clearly unsatisfactory. The paper proposes an alternative learning procedure based on the orthogonal least squares method. The procedure choose radial basis function centers one by one in a rational way until an adequate network has been constructed. The algorithm has the property that each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill-conditioning problems. The orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks, and this is illustrated using examples taken from two different signal processing applications.
Orthogonal least squares learning algorithm for radial basis function networks.
Chen, S; Cowan, C N; Grant, P M
1991-01-01
The radial basis function network offers a viable alternative to the two-layer neural network in many applications of signal processing. A common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular-value decomposition to solve for the weights of the network. Such a procedure has several drawbacks, and, in particular, an arbitrary selection of centers is clearly unsatisfactory. The authors propose an alternative learning procedure based on the orthogonal least-squares method. The procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed. In the algorithm, each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill-conditioning problems. The orthogonal least-squares learning strategy provides a simple and efficient means for fitting radial basis function networks. This is illustrated using examples taken from two different signal processing applications.
Making the most out of the least (squares migration)
Dutta, Gaurav
2014-08-05
Standard migration images can suffer from migration artifacts due to 1) poor source-receiver sampling, 2) weak amplitudes caused by geometric spreading, 3) attenuation, 4) defocusing, 5) poor resolution due to limited source-receiver aperture, and 6) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution. If the migration velocity model is sufficiently accurate, then LSM can mitigate many of the above problems and lead to a more resolved migration image, sometimes with twice the spatial resolution. However, there are two problems with LSM: the cost can be an order of magnitude more than standard migration and the quality of the LSM image is no better than the standard image for velocity errors of 5% or more. We now show how to get the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.
Plane-wave least-squares reverse-time migration
Dai, Wei
2013-06-03
A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reversetime migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors. © 2013 Society of Exploration Geophysicists.
Making the most out of least-squares migration
Huang, Yunsong
2014-09-01
Standard migration images can suffer from (1) migration artifacts caused by an undersampled acquisition geometry, (2) poor resolution resulting from a limited recording aperture, (3) ringing artifacts caused by ripples in the source wavelet, and (4) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly invert seismic data for the reflectivity distribution. Given a sufficiently accurate migration velocity model, LSM can mitigate many of the above problems and can produce more resolved migration images, sometimes with more than twice the spatial resolution of standard migration. However, LSM faces two challenges: The computational cost can be an order of magnitude higher than that of standard migration, and the resulting image quality can fail to improve for migration velocity errors of about 5% or more. It is possible to obtain the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.
Least squares weighted twin support vector machines with local information
Institute of Scientific and Technical Information of China (English)
花小朋; 徐森; 李先锋
2015-01-01
A least squares version of the recently proposed weighted twin support vector machine with local information (WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information (LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.
Kernel-Based Least Squares Temporal Difference With Gradient Correction.
Song, Tianheng; Li, Dazi; Cao, Liulin; Hirasawa, Kotaro
2016-04-01
A least squares temporal difference with gradient correction (LS-TDC) algorithm and its kernel-based version kernel-based LS-TDC (KLS-TDC) are proposed as policy evaluation algorithms for reinforcement learning (RL). LS-TDC is derived from the TDC algorithm. Attributed to TDC derived by minimizing the mean-square projected Bellman error, LS-TDC has better convergence performance. The least squares technique is used to omit the size-step tuning of the original TDC and enhance robustness. For KLS-TDC, since the kernel method is used, feature vectors can be selected automatically. The approximate linear dependence analysis is performed to realize kernel sparsification. In addition, a policy iteration strategy motivated by KLS-TDC is constructed to solve control learning problems. The convergence and parameter sensitivities of both LS-TDC and KLS-TDC are tested through on-policy learning, off-policy learning, and control learning problems. Experimental results, as compared with a series of corresponding RL algorithms, demonstrate that both LS-TDC and KLS-TDC have better approximation and convergence performance, higher efficiency for sample usage, smaller burden of parameter tuning, and less sensitivity to parameters.
Point pattern matching based on kernel partial least squares
Institute of Scientific and Technical Information of China (English)
Weidong Yan; Zheng Tian; Lulu Pan; Jinhuan Wen
2011-01-01
@@ Point pattern matching is an essential step in many image processing applications. This letter investigates the spectral approaches of point pattern matching, and presents a spectral feature matching algorithm based on kernel partial least squares (KPLS). Given the feature points of two images, we define position similarity matrices for the reference and sensed images, and extract the pattern vectors from the matrices using KPLS, which indicate the geometric distribution and the inner relationships of the feature points.Feature points matching are done using the bipartite graph matching method. Experiments conducted on both synthetic and real-world data demonstrate the robustness and invariance of the algorithm.%Point pattern matching is an essential step in many image processing applications. This letter investigates the spectral approaches of point pattern matching, and presents a spectral feature matching algorithm based on kernel partial least squares (KPLS). Given the feature points of two images, we define position similarity matrices for the reference and sensed images, and extract the pattern vectors from the matrices using KPLS, which indicate the geometric distribution and the inner relationships of the feature points.Feature points matching are done using the bipartite graph matching method. Experiments conducted on both synthetic and real-world data demonstrate the robustness and invariance of the algorithm.
Fractional Order Digital Differentiator Design Based on Power Function and Least squares
Kumar, Manjeet; Rawat, Tarun Kumar
2016-10-01
In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald-Letnikov (G-L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G-L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques.
Directory of Open Access Journals (Sweden)
Xisheng Yu
2014-01-01
Full Text Available The paper by Liu (2010 introduces a method termed the canonical least-squares Monte Carlo (CLM which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.
A negative-norm least-squares method for time-harmonic Maxwell equations
Copeland, Dylan M.
2012-04-01
This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.
Kattelans, Thorsten; Heinrichs, Wilhelm
2009-09-01
For Stokes problems least-squares schemes have the big advantage that they require no stabilization and equal order interpolation can be used. The disadvantage of Least-Squares Finite Element Method (LSFEM) and of Least-Squares Spectral Element Method (LSSEM) is that they perform poorly with respect to conservation of mass for internal flow problems, where the LSSEM compensates this by a superior conservation of momentum. In the literature it has been shown that Least-Squares Spectral Collocation Method (LSSCM) leads to superior conservation of mass and momentum for the steady Stokes. Here, we extend the study to the time-dependent Stokes equations for an internal flow problem, where the domain is decomposed into different elements using the transfinite mapping of Gordon and Hall. Minimizing the influence of round-off errors we use QR decomposition for solving the resulting overdetermined algebraic systems instead of forming normal equations.
Regularization Techniques for Linear Least-Squares Problems
Suliman, Mohamed
2016-04-01
Linear estimation is a fundamental branch of signal processing that deals with estimating the values of parameters from a corrupted measured data. Throughout the years, several optimization criteria have been used to achieve this task. The most astonishing attempt among theses is the linear least-squares. Although this criterion enjoyed a wide popularity in many areas due to its attractive properties, it appeared to suffer from some shortcomings. Alternative optimization criteria, as a result, have been proposed. These new criteria allowed, in one way or another, the incorporation of further prior information to the desired problem. Among theses alternative criteria is the regularized least-squares (RLS). In this thesis, we propose two new algorithms to find the regularization parameter for linear least-squares problems. In the constrained perturbation regularization algorithm (COPRA) for random matrices and COPRA for linear discrete ill-posed problems, an artificial perturbation matrix with a bounded norm is forced into the model matrix. This perturbation is introduced to enhance the singular value structure of the matrix. As a result, the new modified model is expected to provide a better stabilize substantial solution when used to estimate the original signal through minimizing the worst-case residual error function. Unlike many other regularization algorithms that go in search of minimizing the estimated data error, the two new proposed algorithms are developed mainly to select the artifcial perturbation bound and the regularization parameter in a way that approximately minimizes the mean-squared error (MSE) between the original signal and its estimate under various conditions. The first proposed COPRA method is developed mainly to estimate the regularization parameter when the measurement matrix is complex Gaussian, with centered unit variance (standard), and independent and identically distributed (i.i.d.) entries. Furthermore, the second proposed COPRA
Least-squares reverse time migration of multiples
Zhang, Dongliang
2013-12-06
The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. For a single source, the entire free-surface becomes an extended virtual source where the downgoing free-surface multiples more fully illuminate the subsurface compared to the primaries. Since each recorded trace is treated as the time history of a virtual source, knowledge of the source wavelet is not required and the ringy time series for each source is automatically deconvolved. If the multiples can be perfectly separated from the primaries, numerical tests on synthetic data for the Sigsbee2B and Marmousi2 models show that least-squares reverse time migration of multiples (LSRTMM) can significantly improve the image quality compared to RTMM or standard reverse time migration (RTM) of primaries. However, if there is imperfect separation and the multiples are strongly interfering with the primaries then LSRTMM images show no significant advantage over the primary migration images. In some cases, they can be of worse quality. Applying LSRTMM to Gulf of Mexico data shows higher signal-to-noise imaging of the salt bottom and top compared to standard RTM images. This is likely attributed to the fact that the target body is just below the sea bed so that the deep water multiples do not have strong interference with the primaries. Migrating a sparsely sampled version of the Marmousi2 ocean bottom seismic data shows that LSM of primaries and LSRTMM provides significantly better imaging than standard RTM. A potential liability of LSRTMM is that multiples require several round trips between the reflector and the free surface, so that high frequencies in the multiples suffer greater attenuation compared to the primary reflections. This can lead to lower
Least-Squares Seismic Inversion with Stochastic Conjugate Gradient Method
Institute of Scientific and Technical Information of China (English)
Wei Huang; Hua-Wei Zhou
2015-01-01
With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.
Local validation of EU-DEM using Least Squares Collocation
Ampatzidis, Dimitrios; Mouratidis, Antonios; Gruber, Christian; Kampouris, Vassilios
2016-04-01
In the present study we are dealing with the evaluation of the European Digital Elevation Model (EU-DEM) in a limited area, covering few kilometers. We compare EU-DEM derived vertical information against orthometric heights obtained by classical trigonometric leveling for an area located in Northern Greece. We apply several statistical tests and we initially fit a surface model, in order to quantify the existing biases and outliers. Finally, we implement a methodology for orthometric heights prognosis, using the Least Squares Collocation for the remaining residuals of the first step (after the fitted surface application). Our results, taking into account cross validation points, reveal a local consistency between EU-DEM and official heights, which is better than 1.4 meters.
Robust Homography Estimation Based on Nonlinear Least Squares Optimization
Directory of Open Access Journals (Sweden)
Wei Mou
2014-01-01
Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.
ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD
Institute of Scientific and Technical Information of China (English)
SONG Kaichen; NIE Xili
2006-01-01
Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion,are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.
A stochastic total least squares solution of adaptive filtering problem.
Javed, Shazia; Ahmad, Noor Atinah
2014-01-01
An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs.
Least-squares based iterative multipath super-resolution technique
Nam, Wooseok
2011-01-01
In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based iterative multipath super-resolution (LIMS). Compared to conventional super-resolution techniques, such as the multiple signal classification (MUSIC) and the estimation of signal parameters via rotation invariance techniques (ESPRIT), our algorithm has several appealing features. In particular, even in critical situations where the conventional super-resolution techniques are not very powerful due to limited data or the correlation between path coefficients, the LIMS algorithm can produce successful results. In addition, due to its iterative nature, the LIMS algorithm is suitable for recursive multipath tracking, whereas the conventional super-resolution techniques may not be. Through numerical simulations, we show that the LIMS algorithm can resolve the first arrival path amo...
Partial Least Squares Structural Equation Modeling with R
Directory of Open Access Journals (Sweden)
Hamdollah Ravand
2016-09-01
Full Text Available Structural equation modeling (SEM has become widespread in educational and psychological research. Its flexibility in addressing complex theoretical models and the proper treatment of measurement error has made it the model of choice for many researchers in the social sciences. Nevertheless, the model imposes some daunting assumptions and restrictions (e.g. normality and relatively large sample sizes that could discourage practitioners from applying the model. Partial least squares SEM (PLS-SEM is a nonparametric technique which makes no distributional assumptions and can be estimated with small sample sizes. In this paper a general introduction to PLS-SEM is given and is compared with conventional SEM. Next, step by step procedures, along with R functions, are presented to estimate the model. A data set is analyzed and the outputs are interpreted
DIRECT ITERATIVE METHODS FOR RANK DEFICIENT GENERALIZED LEAST SQUARES PROBLEMS
Institute of Scientific and Technical Information of China (English)
Jin-yun Yuan; Xiao-qing Jin
2000-01-01
The generalized least squares (LS) problem appears in many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m≥n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well.
Temperature prediction control based on least squares support vector machines
Institute of Scientific and Technical Information of China (English)
Bin LIU; Hongye SU; Weihua HUANG; Jian CHU
2004-01-01
A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity.The nonlinear off-line model of the controlled plant is built by LS-SVM with radial basis function (RBF) kernel.In the process of system running,the off-line model is linearized at each sampling instant,and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant.The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay.The results of the experiment verify the effectiveness and merit of the algorithm.
Regularized plane-wave least-squares Kirchhoff migration
Wang, Xin
2013-09-22
A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.
Partial least squares regression in the social sciences
Directory of Open Access Journals (Sweden)
Megan L. Sawatsky
2015-06-01
Full Text Available Partial least square regression (PLSR is a statistical modeling technique that extracts latent factors to explain both predictor and response variation. PLSR is particularly useful as a data exploration technique because it is highly flexible (e.g., there are few assumptions, variables can be highly collinear. While gaining importance across a diverse number of fields, its application in the social sciences has been limited. Here, we provide a brief introduction to PLSR, directed towards a novice audience with limited exposure to the technique; demonstrate its utility as an alternative to more classic approaches (multiple linear regression, principal component regression; and apply the technique to a hypothetical dataset using JMP statistical software (with references to SAS software.
Least-squares reverse time migration with radon preconditioning
Dutta, Gaurav
2016-09-06
We present a least-squares reverse time migration (LSRTM) method using Radon preconditioning to regularize noisy or severely undersampled data. A high resolution local radon transform is used as a change of basis for the reflectivity and sparseness constraints are applied to the inverted reflectivity in the transform domain. This reflects the prior that for each location of the subsurface the number of geological dips is limited. The forward and the adjoint mapping of the reflectivity to the local Radon domain and back are done through 3D Fourier-based discrete Radon transform operators. The sparseness is enforced by applying weights to the Radon domain components which either vary with the amplitudes of the local dips or are thresholded at given quantiles. Numerical tests on synthetic and field data validate the effectiveness of the proposed approach in producing images with improved SNR and reduced aliasing artifacts when compared with standard RTM or LSRTM.
Cognitive assessment in mathematics with the least squares distance method.
Ma, Lin; Çetin, Emre; Green, Kathy E
2012-01-01
This study investigated the validation of comprehensive cognitive attributes of an eighth-grade mathematics test using the least squares distance method and compared performance on attributes by gender and region. A sample of 5,000 students was randomly selected from the data of the 2005 Turkish national mathematics assessment of eighth-grade students. Twenty-five math items were assessed for presence or absence of 20 cognitive attributes (content, cognitive processes, and skill). Four attributes were found to be misspecified or nonpredictive. However, results demonstrated the validity of cognitive attributes in terms of the revised set of 17 attributes. The girls had similar performance on the attributes as the boys. The students from the two eastern regions significantly underperformed on the most attributes.
A Galerkin least squares approach to viscoelastic flow.
Energy Technology Data Exchange (ETDEWEB)
Rao, Rekha R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schunk, Peter Randall [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-10-01
A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.
Least squares deconvolution of the stellar intensity and polarization spectra
Kochukhov, O; Piskunov, N
2010-01-01
Least squares deconvolution (LSD) is a powerful method of extracting high-precision average line profiles from the stellar intensity and polarization spectra. Despite its common usage, the LSD method is poorly documented and has never been tested using realistic synthetic spectra. In this study we revisit the key assumptions of the LSD technique, clarify its numerical implementation, discuss possible improvements and give recommendations how to make LSD results understandable and reproducible. We also address the problem of interpretation of the moments and shapes of the LSD profiles in terms of physical parameters. We have developed an improved, multiprofile version of LSD and have extended the deconvolution procedure to linear polarization analysis taking into account anomalous Zeeman splitting of spectral lines. This code is applied to the theoretical Stokes parameter spectra. We test various methods of interpreting the mean profiles, investigating how coarse approximations of the multiline technique trans...
RNA structural motif recognition based on least-squares distance.
Shen, Ying; Wong, Hau-San; Zhang, Shaohong; Zhang, Lin
2013-09-01
RNA structural motifs are recurrent structural elements occurring in RNA molecules. RNA structural motif recognition aims to find RNA substructures that are similar to a query motif, and it is important for RNA structure analysis and RNA function prediction. In view of this, we propose a new method known as RNA Structural Motif Recognition based on Least-Squares distance (LS-RSMR) to effectively recognize RNA structural motifs. A test set consisting of five types of RNA structural motifs occurring in Escherichia coli ribosomal RNA is compiled by us. Experiments are conducted for recognizing these five types of motifs. The experimental results fully reveal the superiority of the proposed LS-RSMR compared with four other state-of-the-art methods.
semPLS: Structural Equation Modeling Using Partial Least Squares
Directory of Open Access Journals (Sweden)
Armin Monecke
2012-05-01
Full Text Available Structural equation models (SEM are very popular in many disciplines. The partial least squares (PLS approach to SEM offers an alternative to covariance-based SEM, which is especially suited for situations when data is not normally distributed. PLS path modelling is referred to as soft-modeling-technique with minimum demands regarding mea- surement scales, sample sizes and residual distributions. The semPLS package provides the capability to estimate PLS path models within the R programming environment. Different setups for the estimation of factor scores can be used. Furthermore it contains modular methods for computation of bootstrap confidence intervals, model parameters and several quality indices. Various plot functions help to evaluate the model. The well known mobile phone dataset from marketing research is used to demonstrate the features of the package.
Estimating Military Aircraft Cost Using Least Squares Support Vector Machines
Institute of Scientific and Technical Information of China (English)
ZHU Jia-yuan; ZHANG Xi-bin; ZHANG Heng-xi; REN Bo
2004-01-01
A multi-layer adaptive optimizing parameters algorithm is developed for improving least squares support vector machines(LS-SVM),and a military aircraft life-cycle-cost(LCC)intelligent estimation model is proposed based on the improved LS-SVM.The intelligent cost estimation process is divided into three steps in the model.In the first step,a cost-drive-factor needs to be selected,which is significant for cost estimation.In the second step,military aircraft training samples within costs and cost-drive-factor set are obtained by the LS-SVM.Then the model can be used for new type aircraft cost estimation.Chinese military aircraft costs are estimated in the paper.The results show that the estimated costs by the new model are closer to the true costs than that of the traditionally used methods.
Improved linear least squares estimation using bounded data uncertainty
Ballal, Tarig
2015-04-01
This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.
Risk and Management Control: A Partial Least Square Modelling Approach
DEFF Research Database (Denmark)
Nielsen, Steen; Pontoppidan, Iens Christian
and interrelations between risk and areas within management accounting. The idea is that management accounting should be able to conduct a valid feed forward but also predictions for decision making including risk. This study reports the test of a theoretical model using partial least squares (PLS) on survey data...... and a external attitude dimension. The results have important implications for both management control research and for the management control systems design for the way accountants consider the element of risk in their different tasks, both operational and strategic. Specifically, it seems that different risk......Risk and economic theory goes many year back (e.g. to Keynes & Knight 1921) and risk/uncertainty belong to one of the explanations for the existence of the firm (Coarse, 1937). The present financial crisis going on in the past years have re-accentuated risk and the need of coherence...
Partial Least Squares tutorial for analyzing neuroimaging data
Directory of Open Access Journals (Sweden)
Patricia Van Roon
2014-09-01
Full Text Available Partial least squares (PLS has become a respected and meaningful soft modeling analysis technique that can be applied to very large datasets where the number of factors or variables is greater than the number of observations. Current biometric studies (e.g., eye movements, EKG, body movements, EEG are often of this nature. PLS eliminates the multiple linear regression issues of over-fitting data by finding a few underlying or latent variables (factors that account for most of the variation in the data. In real-world applications, where linear models do not always apply, PLS can model the non-linear relationship well. This tutorial introduces two PLS methods, PLS Correlation (PLSC and PLS Regression (PLSR and their applications in data analysis which are illustrated with neuroimaging examples. Both methods provide straightforward and comprehensible techniques for determining and modeling relationships between two multivariate data blocks by finding latent variables that best describes the relationships. In the examples, the PLSC will analyze the relationship between neuroimaging data such as Event-Related Potential (ERP amplitude averages from different locations on the scalp with their corresponding behavioural data. Using the same data, the PLSR will be used to model the relationship between neuroimaging and behavioural data. This model will be able to predict future behaviour solely from available neuroimaging data. To find latent variables, Singular Value Decomposition (SVD for PLSC and Non-linear Iterative PArtial Least Squares (NIPALS for PLSR are implemented in this tutorial. SVD decomposes the large data block into three manageable matrices containing a diagonal set of singular values, as well as left and right singular vectors. For PLSR, NIPALS algorithms are used because it provides amore precise estimation of the latent variables. Mathematica notebooks are provided for each PLS method with clearly labeled sections and subsections. The
Götterdämmerung over total least squares
Malissiovas, G.; Neitzel, F.; Petrovic, S.
2016-06-01
The traditional way of solving non-linear least squares (LS) problems in Geodesy includes a linearization of the functional model and iterative solution of a nonlinear equation system. Direct solutions for a class of nonlinear adjustment problems have been presented by the mathematical community since the 1980s, based on total least squares (TLS) algorithms and involving the use of singular value decomposition (SVD). However, direct LS solutions for this class of problems have been developed in the past also by geodesists. In this contributionwe attempt to establish a systematic approach for direct solutions of non-linear LS problems from a "geodetic" point of view. Therefore, four non-linear adjustment problems are investigated: the fit of a straight line to given points in 2D and in 3D, the fit of a plane in 3D and the 2D symmetric similarity transformation of coordinates. For all these problems a direct LS solution is derived using the same methodology by transforming the problem to the solution of a quadratic or cubic algebraic equation. Furthermore, by applying TLS all these four problems can be transformed to solving the respective characteristic eigenvalue equations. It is demonstrated that the algebraic equations obtained in this way are identical with those resulting from the LS approach. As a by-product of this research two novel approaches are presented for the TLS solutions of fitting a straight line to 3D and the 2D similarity transformation of coordinates. The derived direct solutions of the four considered problems are illustrated on examples from the literature and also numerically compared to published iterative solutions.
Montgomery, R. C.; Sundararajan, N.
1984-01-01
The basic theory of least square lattice filters and their use in identification of structural dynamics systems is summarized. Thereafter, this theory is applied to a two-dimensional grid structure made of overlapping bars. Previously, this theory has been applied to an integral beam. System identification results are presented for both simulated and experimental tests and they are compared with those predicted using finite element modelling. The lattice filtering approach works well for simulated data based on finite element modelling. However, considerable discrepancy exists between estimates obtained from experimental data and the finite element analysis. It is believed that this discrepancy is the result of inadequacies in the finite element modelling to represent the damped motion of the laboratory apparatus.
Least-Squares Neutron Spectral Adjustment with STAYSL PNNL
Directory of Open Access Journals (Sweden)
Greenwood L.R.
2016-01-01
Full Text Available The STAYSL PNNL computer code, a descendant of the STAY'SL code [1], performs neutron spectral adjustment of a starting neutron spectrum, applying a least squares method to determine adjustments based on saturated activation rates, neutron cross sections from evaluated nuclear data libraries, and all associated covariances. STAYSL PNNL is provided as part of a comprehensive suite of programs [2], where additional tools in the suite are used for assembling a set of nuclear data libraries and determining all required corrections to the measured data to determine saturated activation rates. Neutron cross section and covariance data are taken from the International Reactor Dosimetry File (IRDF-2002 [3], which was sponsored by the International Atomic Energy Agency (IAEA, though work is planned to update to data from the IAEA's International Reactor Dosimetry and Fusion File (IRDFF [4]. The nuclear data and associated covariances are extracted from IRDF-2002 using the third-party NJOY99 computer code [5]. The NJpp translation code converts the extracted data into a library data array format suitable for use as input to STAYSL PNNL. The software suite also includes three utilities to calculate corrections to measured activation rates. Neutron self-shielding corrections are calculated as a function of neutron energy with the SHIELD code and are applied to the group cross sections prior to spectral adjustment, thus making the corrections independent of the neutron spectrum. The SigPhi Calculator is a Microsoft Excel spreadsheet used for calculating saturated activation rates from raw gamma activities by applying corrections for gamma self-absorption, neutron burn-up, and the irradiation history. Gamma self-absorption and neutron burn-up corrections are calculated (iteratively in the case of the burn-up within the SigPhi Calculator spreadsheet. The irradiation history corrections are calculated using the BCF computer code and are inserted into the
Least-Squares Neutron Spectral Adjustment with STAYSL PNNL
Greenwood, L. R.; Johnson, C. D.
2016-02-01
The STAYSL PNNL computer code, a descendant of the STAY'SL code [1], performs neutron spectral adjustment of a starting neutron spectrum, applying a least squares method to determine adjustments based on saturated activation rates, neutron cross sections from evaluated nuclear data libraries, and all associated covariances. STAYSL PNNL is provided as part of a comprehensive suite of programs [2], where additional tools in the suite are used for assembling a set of nuclear data libraries and determining all required corrections to the measured data to determine saturated activation rates. Neutron cross section and covariance data are taken from the International Reactor Dosimetry File (IRDF-2002) [3], which was sponsored by the International Atomic Energy Agency (IAEA), though work is planned to update to data from the IAEA's International Reactor Dosimetry and Fusion File (IRDFF) [4]. The nuclear data and associated covariances are extracted from IRDF-2002 using the third-party NJOY99 computer code [5]. The NJpp translation code converts the extracted data into a library data array format suitable for use as input to STAYSL PNNL. The software suite also includes three utilities to calculate corrections to measured activation rates. Neutron self-shielding corrections are calculated as a function of neutron energy with the SHIELD code and are applied to the group cross sections prior to spectral adjustment, thus making the corrections independent of the neutron spectrum. The SigPhi Calculator is a Microsoft Excel spreadsheet used for calculating saturated activation rates from raw gamma activities by applying corrections for gamma self-absorption, neutron burn-up, and the irradiation history. Gamma self-absorption and neutron burn-up corrections are calculated (iteratively in the case of the burn-up) within the SigPhi Calculator spreadsheet. The irradiation history corrections are calculated using the BCF computer code and are inserted into the SigPhi Calculator
Least-squares joint imaging of multiples and primaries
Brown, Morgan Parker
Current exploration geophysics practice still regards multiple reflections as noise, although multiples often contain considerable information about the earth's angle-dependent reflectivity that primary reflections do not. To exploit this information, multiples and primaries must be combined in a domain in which they are comparable, such as in the prestack image domain. However, unless the multiples and primaries have been pre-separated from the data, crosstalk leakage between multiple and primary images will significantly degrade any gains in the signal fidelity, geologic interpretability, and signal-to-noise ratio of the combined image. I present a global linear least-squares algorithm, denoted LSJIMP (Least-squares Joint Imaging of Multiples and Primaries), which separates multiples from primaries while simultaneously combining their information. The novelty of the method lies in the three model regularization operators which discriminate between crosstalk and signal and extend information between multiple and primary images. The LSJIMP method exploits the hitherto ignored redundancy between primaries and multiples in the data. While many different types of multiple imaging operators are well-suited for use with the LSJIMP method, in this thesis I utilize an efficient prestack time imaging strategy for multiples which sacrifices accuracy in a complex earth for computational speed and convenience. I derive a variant of the normal moveout (NMO) equation for multiples, called HEMNO, which can image "split" pegleg multiples which arise from a moderately heterogeneous earth. I also derive a series of prestack amplitude compensation operators which when combined with HEMNO, transform pegleg multiples into events are directly comparable---kinematically and in terms of amplitudes---to the primary reflection. I test my implementation of LSJIMP on two datasets from the deepwater Gulf of Mexico. The first, a 2-D line in the Mississippi Canyon region, exhibits a variety of
Recursive least squares background prediction of univariate syndromic surveillance data
Directory of Open Access Journals (Sweden)
Burkom Howard
2009-01-01
Full Text Available Abstract Background Surveillance of univariate syndromic data as a means of potential indicator of developing public health conditions has been used extensively. This paper aims to improve the performance of detecting outbreaks by using a background forecasting algorithm based on the adaptive recursive least squares method combined with a novel treatment of the Day of the Week effect. Methods Previous work by the first author has suggested that univariate recursive least squares analysis of syndromic data can be used to characterize the background upon which a prediction and detection component of a biosurvellance system may be built. An adaptive implementation is used to deal with data non-stationarity. In this paper we develop and implement the RLS method for background estimation of univariate data. The distinctly dissimilar distribution of data for different days of the week, however, can affect filter implementations adversely, and so a novel procedure based on linear transformations of the sorted values of the daily counts is introduced. Seven-days ahead daily predicted counts are used as background estimates. A signal injection procedure is used to examine the integrated algorithm's ability to detect synthetic anomalies in real syndromic time series. We compare the method to a baseline CDC forecasting algorithm known as the W2 method. Results We present detection results in the form of Receiver Operating Characteristic curve values for four different injected signal to noise ratios using 16 sets of syndromic data. We find improvements in the false alarm probabilities when compared to the baseline W2 background forecasts. Conclusion The current paper introduces a prediction approach for city-level biosurveillance data streams such as time series of outpatient clinic visits and sales of over-the-counter remedies. This approach uses RLS filters modified by a correction for the weekly patterns often seen in these data series, and a threshold
Nonlinear least-squares data fitting in Excel spreadsheets.
Kemmer, Gerdi; Keller, Sandro
2010-02-01
We describe an intuitive and rapid procedure for analyzing experimental data by nonlinear least-squares fitting (NLSF) in the most widely used spreadsheet program. Experimental data in x/y form and data calculated from a regression equation are inputted and plotted in a Microsoft Excel worksheet, and the sum of squared residuals is computed and minimized using the Solver add-in to obtain the set of parameter values that best describes the experimental data. The confidence of best-fit values is then visualized and assessed in a generally applicable and easily comprehensible way. Every user familiar with the most basic functions of Excel will be able to implement this protocol, without previous experience in data fitting or programming and without additional costs for specialist software. The application of this tool is exemplified using the well-known Michaelis-Menten equation characterizing simple enzyme kinetics. Only slight modifications are required to adapt the protocol to virtually any other kind of dataset or regression equation. The entire protocol takes approximately 1 h.
Improving the gradient in least-squares reverse time migration
Liu, Qiancheng
2016-04-01
Least-squares reverse time migration (LSRTM) is a linearized inversion technique used for estimating high-wavenumber reflectivity. However, due to the redundant overlay of the band-limited source wavelet, the gradient based on the cross-correlated imaging principle suffers from a loss of wavenumber information. We first prepare the residuals between observed and demigrated data by deconvolving with the amplitude spectrum of the source wavelet, and then migrate the preprocessed residuals by using the cross-correlation imaging principle. In this way, a gradient that preserves the spectral signature of data residuals is obtained. The computational cost of source-wavelet removal is negligible compared to that of wavefield simulation. The two-dimensional Marmousi model containing complex geology structures is considered to test our scheme. Numerical examples show that our improved gradient in LSRTM has a better convergence behavior and promises inverted results of higher resolution. Finally, we attempt to update the background velocity with our inverted velocity perturbations to approach the true velocity.
BER analysis of regularized least squares for BPSK recovery
Ben Atitallah, Ismail
2017-06-20
This paper investigates the problem of recovering an n-dimensional BPSK signal x
HASM-AD Algorithm Based on the Sequential Least Squares
Institute of Scientific and Technical Information of China (English)
WANG Shihai; YUE Tianxiang
2010-01-01
The HASM (high accuracy surface modeling) technique is based on the fundamental theory of surfaces, which has been proved to improve the interpolation accuracy in surface fitting. However, the integral iterative solution in previous studies resulted in high temporal complexity in computation and huge memory usage so that it became difficult to put the technique into application,especially for large-scale datasets. In the study, an innovative model (HASM-AD) is developed according to the sequential least squares on the basis of data adjustment theory. Sequential division is adopted in the technique, so that linear equations can be divided into groups to be processed in sequence with the temporal complexity reduced greatly in computation. The experiment indicates that the HASM-AD technique surpasses the traditional spatial interpolation methods in accuracy. Also, the cross-validation result proves the same conclusion for the spatial interpolation of soil PH property with the data sampled in Jiangxi province. Moreover, it is demonstrated in the study that the HASM-AD technique significantly reduces the computational complexity and lessens memory usage in computation.
3D plane-wave least-squares Kirchhoff migration
Wang, Xin
2014-08-05
A three dimensional least-squares Kirchhoff migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images and the computational efficiency. Due to the limitation of current 3D marine acquisition geometries, a cylindrical-wave encoding is adopted for the narrow azimuth streamer data. To account for the mispositioning of reflectors due to errors in the velocity model, a regularized LSM is devised so that each plane-wave or cylindrical-wave gather gives rise to an individual migration image, and a regularization term is included to encourage the similarities between the migration images of similar encoding schemes. Both synthetic and field results show that: 1) plane-wave or cylindrical-wave encoding LSM can achieve both computational and IO saving, compared to shot-domain LSM, however, plane-wave LSM is still about 5 times more expensive than plane-wave migration; 2) the regularized LSM is more robust compared to LSM with one reflectivity model common for all the plane-wave or cylindrical-wave gathers.
Non-linear Least Squares Fitting in IDL with MPFIT
Markwardt, Craig B
2009-01-01
MPFIT is a port to IDL of the non-linear least squares fitting program MINPACK-1. MPFIT inherits the robustness of the original FORTRAN version of MINPACK-1, but is optimized for performance and convenience in IDL. In addition to the main fitting engine, MPFIT, several specialized functions are provided to fit 1-D curves and 2-D images; 1-D and 2-D peaks; and interactive fitting from the IDL command line. Several constraints can be applied to model parameters, including fixed constraints, simple bounding constraints, and "tying" the value to another parameter. Several data weighting methods are allowed, and the parameter covariance matrix is computed. Extensive diagnostic capabilities are available during the fit, via a call-back subroutine, and after the fit is complete. Several different forms of documentation are provided, including a tutorial, reference pages, and frequently asked questions. The package has been translated to C and Python as well. The full IDL and C packages can be found at http://purl.co...
Suppressing Anomalous Localized Waffle Behavior in Least Squares Wavefront Reconstructors
Energy Technology Data Exchange (ETDEWEB)
Gavel, D
2002-10-08
A major difficulty with wavefront slope sensors is their insensitivity to certain phase aberration patterns, the classic example being the waffle pattern in the Fried sampling geometry. As the number of degrees of freedom in AO systems grows larger, the possibility of troublesome waffle-like behavior over localized portions of the aperture is becoming evident. Reconstructor matrices have associated with them, either explicitly or implicitly, an orthogonal mode space over which they operate, called the singular mode space. If not properly preconditioned, the reconstructor's mode set can consist almost entirely of modes that each have some localized waffle-like behavior. In this paper we analyze the behavior of least-squares reconstructors with regard to their mode spaces. We introduce a new technique that is successful in producing a mode space that segregates the waffle-like behavior into a few ''high order'' modes, which can then be projected out of the reconstructor matrix. This technique can be adapted so as to remove any specific modes that are undesirable in the final reconstructor (such as piston, tip, and tilt for example) as well as suppress (the more nebulously defined) localized waffle behavior.
Efficient sparse kernel feature extraction based on partial least squares.
Dhanjal, Charanpal; Gunn, Steve R; Shawe-Taylor, John
2009-08-01
The presence of irrelevant features in training data is a significant obstacle for many machine learning tasks. One approach to this problem is to extract appropriate features and, often, one selects a feature extraction method based on the inference algorithm. Here, we formalize a general framework for feature extraction, based on Partial Least Squares, in which one can select a user-defined criterion to compute projection directions. The framework draws together a number of existing results and provides additional insights into several popular feature extraction methods. Two new sparse kernel feature extraction methods are derived under the framework, called Sparse Maximal Alignment (SMA) and Sparse Maximal Covariance (SMC), respectively. Key advantages of these approaches include simple implementation and a training time which scales linearly in the number of examples. Furthermore, one can project a new test example using only k kernel evaluations, where k is the output dimensionality. Computational results on several real-world data sets show that SMA and SMC extract features which are as predictive as those found using other popular feature extraction methods. Additionally, on large text retrieval and face detection data sets, they produce features which match the performance of the original ones in conjunction with a Support Vector Machine.
Prediction of solubility parameters using partial least square regression.
Tantishaiyakul, Vimon; Worakul, Nimit; Wongpoowarak, Wibul
2006-11-15
The total solubility parameter (delta) values were effectively predicted by using computed molecular descriptors and multivariate partial least squares (PLS) statistics. The molecular descriptors in the derived models included heat of formation, dipole moment, molar refractivity, solvent-accessible surface area (SA), surface-bounded molecular volume (SV), unsaturated index (Ui), and hydrophilic index (Hy). The values of these descriptors were computed by the use of HyperChem 7.5, QSPR Properties module in HyperChem 7.5, and Dragon Web version. The other two descriptors, hydrogen bonding donor (HD), and hydrogen bond-forming ability (HB) were also included in the models. The final reduced model of the whole data set had R(2) of 0.853, Q(2) of 0.813, root mean squared error from the cross-validation of the training set (RMSEcv(tr)) of 2.096 and RMSE of calibration (RMSE(tr)) of 1.857. No outlier was observed from this data set of 51 diverse compounds. Additionally, the predictive power of the developed model was comparable to the well recognized systems of Hansen, van Krevelen and Hoftyzer, and Hoy.
River flow time series using least squares support vector machines
Samsudin, R.; Saad, P.; Shabri, A.
2011-06-01
This paper proposes a novel hybrid forecasting model known as GLSSVM, which combines the group method of data handling (GMDH) and the least squares support vector machine (LSSVM). The GMDH is used to determine the useful input variables which work as the time series forecasting for the LSSVM model. Monthly river flow data from two stations, the Selangor and Bernam rivers in Selangor state of Peninsular Malaysia were taken into consideration in the development of this hybrid model. The performance of this model was compared with the conventional artificial neural network (ANN) models, Autoregressive Integrated Moving Average (ARIMA), GMDH and LSSVM models using the long term observations of monthly river flow discharge. The root mean square error (RMSE) and coefficient of correlation (R) are used to evaluate the models' performances. In both cases, the new hybrid model has been found to provide more accurate flow forecasts compared to the other models. The results of the comparison indicate that the new hybrid model is a useful tool and a promising new method for river flow forecasting.
Least-squares fit of a linear combination of functions
Directory of Open Access Journals (Sweden)
Niraj Upadhyay
2013-12-01
Full Text Available We propose that given a data-set $S=\\{(x_i,y_i/i=1,2,{\\dots}n\\}$ and real-valued functions $\\{f_\\alpha(x/\\alpha=1,2,{\\dots}m\\},$ the least-squares fit vector $A=\\{a_\\alpha\\}$ for $y=\\sum_\\alpha a_{\\alpha}f_\\alpha(x$ is $A = (F^TF^{-1}F^TY$ where $[F_{i\\alpha}]=[f_\\alpha(x_i].$ We test this formalism by deriving the algebraic expressions of the regression coefficients in $y = ax + b$ and in $y = ax^2 + bx + c.$ As a practical application, we successfully arrive at the coefficients in the semi-empirical mass formula of nuclear physics. The formalism is {\\it generic} - it has the potential of being applicable to any {\\it type} of $\\{x_i\\}$ as long as there exist appropriate $\\{f_\\alpha\\}.$ The method can be exploited with a CAS or an object-oriented language and is excellently suitable for parallel-processing.
A Novel Kernel for Least Squares Support Vector Machine
Institute of Scientific and Technical Information of China (English)
FENG Wei; ZHAO Yong-ping; DU Zhong-hua; LI De-cai; WANG Li-feng
2012-01-01
Extreme learning machine(ELM) has attracted much attention in recent years due to its fast convergence and good performance.Merging both ELM and support vector machine is an important trend,thus yielding an ELM kernel.ELM kernel based methods are able to solve the nonlinear problems by inducing an explicit mapping compared with the commonly-used kernels such as Gaussian kernel.In this paper,the ELM kernel is extended to the least squares support vector regression(LSSVR),so ELM-LSSVR was proposed.ELM-LSSVR can be used to reduce the training and test time simultaneously without extra techniques such as sequential minimal optimization and pruning mechanism.Moreover,the memory space for the training and test was relieved.To confirm the efficacy and feasibility of the proposed ELM-LSSVR,the experiments are reported to demonstrate that ELM-LSSVR takes the advantage of training and test time with comparable accuracy to other algorithms.
Robust regularized least-squares beamforming approach to signal estimation
Suliman, Mohamed
2017-05-12
In this paper, we address the problem of robust adaptive beamforming of signals received by a linear array. The challenge associated with the beamforming problem is twofold. Firstly, the process requires the inversion of the usually ill-conditioned covariance matrix of the received signals. Secondly, the steering vector pertaining to the direction of arrival of the signal of interest is not known precisely. To tackle these two challenges, the standard capon beamformer is manipulated to a form where the beamformer output is obtained as a scaled version of the inner product of two vectors. The two vectors are linearly related to the steering vector and the received signal snapshot, respectively. The linear operator, in both cases, is the square root of the covariance matrix. A regularized least-squares (RLS) approach is proposed to estimate these two vectors and to provide robustness without exploiting prior information. Simulation results show that the RLS beamformer using the proposed regularization algorithm outperforms state-of-the-art beamforming algorithms, as well as another RLS beamformers using a standard regularization approaches.
Parsimonious extreme learning machine using recursive orthogonal least squares.
Wang, Ning; Er, Meng Joo; Han, Min
2014-10-01
Novel constructive and destructive parsimonious extreme learning machines (CP- and DP-ELM) are proposed in this paper. By virtue of the proposed ELMs, parsimonious structure and excellent generalization of multiinput-multioutput single hidden-layer feedforward networks (SLFNs) are obtained. The proposed ELMs are developed by innovative decomposition of the recursive orthogonal least squares procedure into sequential partial orthogonalization (SPO). The salient features of the proposed approaches are as follows: 1) Initial hidden nodes are randomly generated by the ELM methodology and recursively orthogonalized into an upper triangular matrix with dramatic reduction in matrix size; 2) the constructive SPO in the CP-ELM focuses on the partial matrix with the subcolumn of the selected regressor including nonzeros as the first column while the destructive SPO in the DP-ELM operates on the partial matrix including elements determined by the removed regressor; 3) termination criteria for CP- and DP-ELM are simplified by the additional residual error reduction method; and 4) the output weights of the SLFN need not be solved in the model selection procedure and is derived from the final upper triangular equation by backward substitution. Both single- and multi-output real-world regression data sets are used to verify the effectiveness and superiority of the CP- and DP-ELM in terms of parsimonious architecture and generalization accuracy. Innovative applications to nonlinear time-series modeling demonstrate superior identification results.
A pruning method for the recursive least squared algorithm.
Leung, C S; Wong, K W; Sum, P F; Chan, L W
2001-03-01
The recursive least squared (RLS) algorithm is an effective online training method for neural networks. However, its conjunctions with weight decay and pruning have not been well studied. This paper elucidates how generalization ability can be improved by selecting an appropriate initial value of the error covariance matrix in the RLS algorithm. Moreover, how the pruning of neural networks can be benefited by using the final value of the error covariance matrix will also be investigated. Our study found that the RLS algorithm is implicitly a weight decay method, where the weight decay effect is controlled by the initial value of the error covariance matrix; and that the inverse of the error covariance matrix is approximately equal to the Hessian matrix of the network being trained. We propose that neural networks are first trained by the RLS algorithm and then some unimportant weights are removed based on the approximate Hessian matrix. Simulation results show that our approach is an effective training and pruning method for neural networks.
Non-parametric and least squares Langley plot methods
Directory of Open Access Journals (Sweden)
P. W. Kiedron
2015-04-01
Full Text Available Langley plots are used to calibrate sun radiometers primarily for the measurement of the aerosol component of the atmosphere that attenuates (scatters and absorbs incoming direct solar radiation. In principle, the calibration of a sun radiometer is a straightforward application of the Bouguer–Lambert–Beer law V=V>/i>0e−τ ·m, where a plot of ln (V voltage vs. m air mass yields a straight line with intercept ln (V0. This ln (V0 subsequently can be used to solve for τ for any measurement of V and calculation of m. This calibration works well on some high mountain sites, but the application of the Langley plot calibration technique is more complicated at other, more interesting, locales. This paper is concerned with ferreting out calibrations at difficult sites and examining and comparing a number of conventional and non-conventional methods for obtaining successful Langley plots. The eleven techniques discussed indicate that both least squares and various non-parametric techniques produce satisfactory calibrations with no significant differences among them when the time series of ln (V0's are smoothed and interpolated with median and mean moving window filters.
PREDIKSI WAKTU KETAHANAN HIDUP DENGAN METODE PARTIAL LEAST SQUARE
Directory of Open Access Journals (Sweden)
PANDE PUTU BUDI KUSUMA
2013-03-01
Full Text Available Coronary heart disease is caused due to an accumulation of fat on the inside walls of blood vessels of the heart (coronary arteries. The factors that had led to the occurrence of coronary heart disease is dominated by unhealthy lifestyle of patients, and the survival times of different patients. This research objective is to predict the survival time of patients with coronary heart disease by taking into account the explanatory variables were analyzed by the method of Partial Least Square (PLS. PLS method is used to resolve the multiple regression analysis when the specific problems of multicollinearity and microarray data. The purpose of the PLS method is to predict the explanatory variables with multiple response variables so as to produce a more accurate predictive value. The results of this research showed that the prediction of survival for the three samples of patients with coronary heart disease had an average of 13 days, with a RMSEP value (error value was 1.526 which means that the results of this study are not much different from the predicted results in the field of medicine. This is consistent with the fact that the medical field suggests that the average survival for patients with coronary heart disease by 13 days.
Laboure, Vincent M.; McClarren, Ryan G.; Wang, Yaqi
2016-01-01
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares (LS) form of the transport equation in the void regions and the Self-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation need a correction in void. The price to pay for this fix is the loss of sy...
A Pascal program for the least-squares evaluation of standard RBS spectra
Hnatowicz, V.; Havránek, V.; Kvítek, J.
1992-11-01
A computer program for least-squares fitting of energy spectra obtained in common Rutherford backscattering (RBS) analyses is described. The samples analyzed by RBS technique are considered to be made up of a finite number of layers, each with uniform composition. The RBS spectra are treated as a combination of variable number of three different basic figures (strip, bulge and Gaussian) which are represented by ad-hoc chosen analytical expressions. The initial parameter estimates are inserted by the operator (with an assistance of graphical support on a TV screen) and the result of the fit is displayed on the screen and stored as a table on hard disk.
Fast Dating Using Least-Squares Criteria and Algorithms.
To, Thu-Hien; Jung, Matthieu; Lycett, Samantha; Gascuel, Olivier
2016-01-01
Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses (e.g., human immunodeficiency virus (HIV)). Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley-Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes. When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint). Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint (i.e., an ancestral node must be older that its daughter nodes) is accounted for. With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time. With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa). In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees. We compare these algorithms to standard methods (root-to-tip, r8s version of Langley-Fitch method, and BEAST). Using simulated data, we show that their estimation accuracy is similar to that
Least squares in calibration: dealing with uncertainty in x.
Tellinghuisen, Joel
2010-08-01
The least-squares (LS) analysis of data with error in x and y is generally thought to yield best results when carried out by minimizing the "total variance" (TV), defined as the sum of the properly weighted squared residuals in x and y. Alternative "effective variance" (EV) methods project the uncertainty in x into an effective contribution to that in y, and though easier to employ are considered to be less reliable. In the case of a linear response function with both sigma(x) and sigma(y) constant, the EV solutions are identically those from ordinary LS; and Monte Carlo (MC) simulations reveal that they can actually yield smaller root-mean-square errors than the TV method. Furthermore, the biases can be predicted from theory based on inverse regression--x upon y when x is error-free and y is uncertain--which yields a bias factor proportional to the ratio sigma(x)(2)/sigma(xm)(2) of the random-error variance in x to the model variance. The MC simulations confirm that the biases are essentially independent of the error in y, hence correctable. With such bias corrections, the better performance of the EV method in estimating the parameters translates into better performance in estimating the unknown (x(0)) from measurements (y(0)) of its response. The predictability of the EV parameter biases extends also to heteroscedastic y data as long as sigma(x) remains constant, but the estimation of x(0) is not as good in this case. When both x and y are heteroscedastic, there is no known way to predict the biases. However, the MC simulations suggest that for proportional error in x, a geometric x-structure leads to small bias and comparable performance for the EV and TV methods.
Topology testing of phylogenies using least squares methods
Directory of Open Access Journals (Sweden)
Wróbel Borys
2006-12-01
Full Text Available Abstract Background The least squares (LS method for constructing confidence sets of trees is closely related to LS tree building methods, in which the goodness of fit of the distances measured on the tree (patristic distances to the observed distances between taxa is the criterion used for selecting the best topology. The generalized LS (GLS method for topology testing is often frustrated by the computational difficulties in calculating the covariance matrix and its inverse, which in practice requires approximations. The weighted LS (WLS allows for a more efficient albeit approximate calculation of the test statistic by ignoring the covariances between the distances. Results The goal of this paper is to assess the applicability of the LS approach for constructing confidence sets of trees. We show that the approximations inherent to the WLS method did not affect negatively the accuracy and reliability of the test both in the analysis of biological sequences and DNA-DNA hybridization data (for which character-based testing methods cannot be used. On the other hand, we report several problems for the GLS method, at least for the available implementation. For many data sets of biological sequences, the GLS statistic could not be calculated. For some data sets for which it could, the GLS method included all the possible trees in the confidence set despite a strong phylogenetic signal in the data. Finally, contrary to WLS, for simulated sequences GLS showed undercoverage (frequent non-inclusion of the true tree in the confidence set. Conclusion The WLS method provides a computationally efficient approximation to the GLS useful especially in exploratory analyses of confidence sets of trees, when assessing the phylogenetic signal in the data, and when other methods are not available.
The moving-least-squares-particle hydrodynamics method (MLSPH)
Energy Technology Data Exchange (ETDEWEB)
Dilts, G. [Los Alamos National Lab., NM (United States)
1997-12-31
An enhancement of the smooth-particle hydrodynamics (SPH) method has been developed using the moving-least-squares (MLS) interpolants of Lancaster and Salkauskas which simultaneously relieves the method of several well-known undesirable behaviors, including spurious boundary effects, inaccurate strain and rotation rates, pressure spikes at impact boundaries, and the infamous tension instability. The classical SPH method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of motion for continua using as basis functions the SPH kernel function multiplied by the particle volume. This derivation is then modified by simply substituting the MLS interpolants for the SPH Galerkin basis, taking care to redefine the particle volume and mass appropriately. The familiar SPH kernel approximation is now equivalent to a colocation-Galerkin method. Both classical conservative and recent non-conservative formulations of SPH can be derived and emulated. The non-conservative forms can be made conservative by adding terms that are zero within the approximation at the expense of boundary-value considerations. The familiar Monaghan viscosity is used. Test calculations of uniformly expanding fluids, the Swegle example, spinning solid disks, impacting bars, and spherically symmetric flow illustrate the superiority of the technique over SPH. In all cases it is seen that the marvelous ability of the MLS interpolants to add up correctly everywhere civilizes the noisy, unpredictable nature of SPH. Being a relatively minor perturbation of the SPH method, it is easily retrofitted into existing SPH codes. On the down side, computational expense at this point is significant, the Monaghan viscosity undoes the contribution of the MLS interpolants, and one-point quadrature (colocation) is not accurate enough. Solutions to these difficulties are being pursued vigorously.
Integer least-squares theory for the GNSS compass
Teunissen, P. J. G.
2010-07-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory
Analyzing industrial energy use through ordinary least squares regression models
Golden, Allyson Katherine
Extensive research has been performed using regression analysis and calibrated simulations to create baseline energy consumption models for residential buildings and commercial institutions. However, few attempts have been made to discuss the applicability of these methodologies to establish baseline energy consumption models for industrial manufacturing facilities. In the few studies of industrial facilities, the presented linear change-point and degree-day regression analyses illustrate ideal cases. It follows that there is a need in the established literature to discuss the methodologies and to determine their applicability for establishing baseline energy consumption models of industrial manufacturing facilities. The thesis determines the effectiveness of simple inverse linear statistical regression models when establishing baseline energy consumption models for industrial manufacturing facilities. Ordinary least squares change-point and degree-day regression methods are used to create baseline energy consumption models for nine different case studies of industrial manufacturing facilities located in the southeastern United States. The influence of ambient dry-bulb temperature and production on total facility energy consumption is observed. The energy consumption behavior of industrial manufacturing facilities is only sometimes sufficiently explained by temperature, production, or a combination of the two variables. This thesis also provides methods for generating baseline energy models that are straightforward and accessible to anyone in the industrial manufacturing community. The methods outlined in this thesis may be easily replicated by anyone that possesses basic spreadsheet software and general knowledge of the relationship between energy consumption and weather, production, or other influential variables. With the help of simple inverse linear regression models, industrial manufacturing facilities may better understand their energy consumption and
Institute of Scientific and Technical Information of China (English)
Sang Dong Kim; Byeong Chun Shin; Seokchan Kim; Gyungsoo Woo
2003-01-01
This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed leastsquares functional is defined as the sum of the L2- and H-1-norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.
Huang, Yunsong
2012-05-22
Multisource migration of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. The accompanying crosstalk noise, in addition to the migration footprint, can be reduced by least-squares inversion. But the application of this approach to marine streamer data is hampered by the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modelling method. This leads to a strong mismatch in the misfit function and results in strong artefacts (crosstalk) in the multisource least-squares migration image. To eliminate this noise, we present a frequency-division multiplexing (FDM) strategy with iterative least-squares migration (ILSM) of supergathers. The key idea is, at each ILSM iteration, to assign a unique frequency band to each shot gather. In this case there is no overlap in the crosstalk spectrum of each migrated shot gather m(x, ω i), so the spectral crosstalk product m(x, ω i)m(x, ω j) =δ i, j is zero, unless i=j. Our results in applying this method to 2D marine data for a SEG/EAGE salt model show better resolved images than standard migration computed at about 1/10 th of the cost. Similar results are achieved after applying this method to synthetic data for a 3D SEG/EAGE salt model, except the acquisition geometry is similar to that of a marine OBS survey. Here, the speedup of this method over conventional migration is more than 10. We conclude that multisource migration for a marine geometry can be successfully achieved by a frequency-division encoding strategy, as long as crosstalk-prone sources are segregated in their spectral content. This is both the strength and the potential limitation of this method. © 2012 European Association of Geoscientists & Engineers.
Hays, J. R.
1969-01-01
Lumped parametric system models are simplified and computationally advantageous in the frequency domain of linear systems. Nonlinear least squares computer program finds the least square best estimate for any number of parameters in an arbitrarily complicated model.
Least Square Methods for Solving Systems of Inequalities with Application to an Assignment Problem
1992-11-01
problem using continuous methods and (2) solving systems of inequalities (and equalities) in a least square sense. The specific assignment problem has...linear equations, in a least square sense are developed. Common algorithmic approaches to solve nonlinear least square problems are adapted to solve
Zhao, Hanxue; Zhou, Zhenggan; Fan, Jin; Li, Gen; Sun, Guangkai
2017-02-01
This paper reports the application of the least-squares regression method in the step-heating thermographic inspection of steel structures. The surface temperature variation of a slab with finite thickness during both the step-heating phase and the cooling-down phase is presented. A mild steel slab with holes of various depths and diameters is chosen as the specimen. The step-heating thermographic inspection experiments are carried out on the specimen with different heating times. The heating as well as the cooling-down phases are recorded with an infrared camera and are analyzed separately by linear regression of the double logarithmic temperature increase versus time plots. Three statistics of the linear regression, the slope, the coefficient of determination, and the F-test value, are used to create image maps according to the processing results. The signal-to-noise ratio of each map is calculated to evaluate the performance of the three imaging methods with different durations of heating time and cooling time. The results prove that the F-test value maps present a good performance for the sequences of the step-heating phase, while the slope maps present a good performance for the sequences of the cooling-down phase. The optimal heating time and cooling time for a steel structure are also concluded. The comparison with the results of the thermographic signal reconstruction (TSR) method proves that the least-squares regression method has better detectability and a higher inspection efficiency.
Distributed weighted least-squares estimation with fast convergence for large-scale systems.
Marelli, Damián Edgardo; Fu, Minyue
2015-01-01
In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.
First-order system least squares for the pure traction problem in planar linear elasticity
Energy Technology Data Exchange (ETDEWEB)
Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.
1996-12-31
This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.
Institute of Scientific and Technical Information of China (English)
Kal Long; Zhengxing Zuo; Rehan H.Zuberi
2009-01-01
This paper presents a new approach to the structural topology optimization of con-tinuum structures. Material-point independent variables are presented to illustrate the existence condition, or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses, not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field, but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points, scaling parameter, weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the pro-posed method. The method is found robust and no numerical instabilities are found with proper parameters.
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2013-05-21
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.
Liu, Jingwei; Liu, Yi; Xu, Meizhi
2015-01-01
Parameter estimation method of Jelinski-Moranda (JM) model based on weighted nonlinear least squares (WNLS) is proposed. The formulae of resolving the parameter WNLS estimation (WNLSE) are derived, and the empirical weight function and heteroscedasticity problem are discussed. The effects of optimization parameter estimation selection based on maximum likelihood estimation (MLE) method, least squares estimation (LSE) method and weighted nonlinear least squares estimation (WNLSE) method are al...
CHEBYSHEV WEIGHTED NORM LEAST-SQUARES SPECTRAL METHODS FOR THE ELLIPTIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Sang Dong Kim; Byeong Chun Shin
2006-01-01
We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the L2w-and H-1w,- norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.
Directory of Open Access Journals (Sweden)
Zhan-bo Chen
2014-01-01
Full Text Available In order to improve the performance prediction accuracy of hydraulic excavator, the regression least squares support vector machine is applied. First, the mathematical model of the regression least squares support vector machine is studied, and then the algorithm of the regression least squares support vector machine is designed. Finally, the performance prediction simulation of hydraulic excavator based on regression least squares support vector machine is carried out, and simulation results show that this method can predict the performance changing rules of hydraulic excavator correctly.
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Speckle evolution with multiple steps of least-squares phase removal
CSIR Research Space (South Africa)
Chen, M
2011-08-01
Full Text Available The authors study numerically the evolution of speckle fields due to the annihilation of optical vortices after the least-squares phase has been removed. A process with multiple steps of least-squares phase removal is carried out to minimize both...
Least-Squares Mirrorsymmetric Solution for Matrix Equations (AX=B, XC=D)
Institute of Scientific and Technical Information of China (English)
Fanliang Li; Xiyan Hu; Lei Zhang
2006-01-01
In this paper, least-squares mirrorsymmetric solution for matrix equations (AX =B, XC=D) and its optimal approximation is considered. With special expression of mirrorsymmetric matrices, a general representation of solution for the least-squares problem is obtained. In addition, the optimal approximate solution and some algorithms to obtain the optimal approximation are provided.
A Generalized Autocovariance Least-Squares Method for Kalman Filter Tuning
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad
2008-01-01
of the state estimates. There is a linear relationship between covariances and autocovariance. Therefore, the covariance estimation problem can be stated as a least-squares problem, which can be solved as a symmetric semidefinite least-squares problem. This problem is convex and can be solved efficiently...
A Simple Introduction to Moving Least Squares and Local Regression Estimation
Energy Technology Data Exchange (ETDEWEB)
Garimella, Rao Veerabhadra [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-06-22
In this brief note, a highly simpli ed introduction to esimating functions over a set of particles is presented. The note starts from Global Least Squares tting, going on to Moving Least Squares estimation (MLS) and nally, Local Regression Estimation (LRE).
Calculation of stratum surface principal curvature based on a moving least square method
Institute of Scientific and Technical Information of China (English)
LI Guo-qing; MENG Zhao-ping; MA Feng-shan; ZHAO Hai-jun; DING De-min; LIU Qin; WANG Cheng
2008-01-01
With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribu-tion of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.
Liu, Jingwei
2011-01-01
A function based nonlinear least squares estimation (FNLSE) method is proposed and investigated in parameter estimation of Jelinski-Moranda software reliability model. FNLSE extends the potential fitting functions of traditional least squares estimation (LSE), and takes the logarithm transformed nonlinear least squares estimation (LogLSE) as a special case. A novel power transformation function based nonlinear least squares estimation (powLSE) is proposed and applied to the parameter estimation of Jelinski-Moranda model. Solved with Newton-Raphson method, Both LogLSE and powLSE of Jelinski-Moranda models are applied to the mean time between failures (MTBF) predications on six standard software failure time data sets. The experimental results demonstrate the effectiveness of powLSE with optimal power index compared to the classical least--squares estimation (LSE), maximum likelihood estimation (MLE) and LogLSE in terms of recursively relative error (RE) index and Braun statistic index.
Gu, Fanglin; Zhang, Hang; Wang, Wenwu; Zhu, Desheng
2013-12-01
Generating function (GF) has been used in blind identification for real-valued signals. In this paper, the definition of GF is first generalized for complex-valued random variables in order to exploit the statistical information carried on complex signals in a more effective way. Then an algebraic structure is proposed to identify the mixing matrix from underdetermined mixtures using the generalized generating function (GGF). Two methods, namely GGF-ALS and GGF-TALS, are developed for this purpose. In the GGF-ALS method, the mixing matrix is estimated by the decomposition of the tensor constructed from the Hessian matrices of the GGF of the observations, using an alternating least squares (ALS) algorithm. The GGF-TALS method is an improved version of the GGF-ALS algorithm based on Tucker decomposition. More specifically, the original tensor, as formed in GGF-ALS, is first converted to a lower-rank core tensor using the Tucker decomposition, where the factors are obtained by the left singular-value decomposition of the original tensor's mode-3 matrix. Then the mixing matrix is estimated by decomposing the core tensor with the ALS algorithm. Simulation results show that (a) the proposed GGF-ALS and GGF-TALS approaches have almost the same performance in terms of the relative errors, whereas the GGF-TALS has much lower computational complexity, and (b) the proposed GGF algorithms have superior performance to the latest GF-based baseline approaches.
Institute of Scientific and Technical Information of China (English)
水庆象; 王大国
2014-01-01
A method for simulation of unsteady incompressible N-S (Navier-Stokes) equations is presen-ted .In the each time step ,the N-S equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm .For the diffusive equation ,the temporal discretization is per-formed by the backward difference method and the spatial discretization is performed by the standard Galerkin method .For the convective equation ,it is the first-order nonlinear partial differential equation ;the temporal discretizaton is also performed by the backward difference method and Newton’s method for the linearization of the nonlinear part .The spatial discretization is performed by the least square scheme and the resulting matrix is symmetric and positive definite .T he driven square flow and flow over a circular cylinder are conducted to validate .Numerical results agree well with benchmark solution for the simulations of the driven square flow .Especially ,for the flow over a circular cylinder ,the numerical results such as the forces of cylinder ,Strouhal number and the pressure on the cylinder surface agree well with experimental and numerical results ,which prove that it can exactly and reliably to simulate the characteristics of flow over a circular cylinder in laminar flow .%采用最小二乘算子分裂有限元法求解非定常不可压N-S（Navier-Stokes）方程，即在每个时间层上采用算子分裂法将N-S方程分裂成扩散项和对流项，这样既能考虑对流占优特点又能顾及方程的扩散性质。扩散项是一个抛物型方程，时间离散采用向后差分格式，空间离散采用标准Galerkin有限元法。对流项的时间项采用后向差分格式，非线性部分用牛顿法进行线性化处理，再用最小二乘有限元法进行空间离散，得到对称正定的代数方程组系数矩阵。采用Re＝1000的方腔流对该算法的有效性进行检验，表明其具有较高的精度，
Laboure, Vincent M; Wang, Yaqi
2016-01-01
In this paper, we derive a method for the second-order form of the transport equation that is both globally conservative and compatible with voids, using Continuous Finite Element Methods (CFEM). The main idea is to use the Least-Squares (LS) form of the transport equation in the void regions and the Self-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation is globally conservative, the LS formulation need a correction in void. The price to pay for this fix is the loss of symmetry of the bilinear form. We first derive this Conservative LS (CLS) formulation in void. Second we combine the SAAF and CLS forms and end up with an hybrid SAAF-CLS method, having the desired properties. We show that extending the theory to near-void regions is a minor complication and can be done without affecting the global conservation of the scheme. Being angular discretization agnostic, this method can be applied to both discrete ordinates (SN) and spherical harmonics (PN) methods. However, since a globally conse...
Fishery landing forecasting using EMD-based least square support vector machine models
Shabri, Ani
2015-05-01
In this paper, the novel hybrid ensemble learning paradigm integrating ensemble empirical mode decomposition (EMD) and least square support machine (LSSVM) is proposed to improve the accuracy of fishery landing forecasting. This hybrid is formulated specifically to address in modeling fishery landing, which has high nonlinear, non-stationary and seasonality time series which can hardly be properly modelled and accurately forecasted by traditional statistical models. In the hybrid model, EMD is used to decompose original data into a finite and often small number of sub-series. The each sub-series is modeled and forecasted by a LSSVM model. Finally the forecast of fishery landing is obtained by aggregating all forecasting results of sub-series. To assess the effectiveness and predictability of EMD-LSSVM, monthly fishery landing record data from East Johor of Peninsular Malaysia, have been used as a case study. The result shows that proposed model yield better forecasts than Autoregressive Integrated Moving Average (ARIMA), LSSVM and EMD-ARIMA models on several criteria..
An Effective Hybrid Artificial Bee Colony Algorithm for Nonnegative Linear Least Squares Problems
Directory of Open Access Journals (Sweden)
Xiangyu Kong
2014-07-01
Full Text Available An effective hybrid artificial bee colony algorithm is proposed in this paper for nonnegative linear least squares problems. To further improve the performance of algorithm, orthogonal initialization method is employed to generate the initial swarm. Furthermore, to balance the exploration and exploitation abilities, a new search mechanism is designed. The performance of this algorithm is verified by using 27 benchmark functions and 5 nonnegative linear least squares test problems. And the comparison analyses are given between the proposed algorithm and other swarm intelligence algorithms. Numerical results demonstrate that the proposed algorithm displays a high performance compared with other algorithms for global optimization problems and nonnegative linear least squares problems.
On the interpretation of least squares collocation. [for geodetic data reduction
Tapley, B. D.
1976-01-01
A demonstration is given of the strict mathematical equivalence between the least squares collocation and the classical minimum variance estimates. It is shown that the least squares collocation algorithms are a special case of the modified minimum variance estimates. The computational efficiency of several forms of the general minimum variance estimation algorithm is discussed. It is pointed out that for certain geodetic applications the least square collocation algorithm may provide a more efficient formulation of the results from the point of view of the computations required.
DEFF Research Database (Denmark)
Anders, Annett; Nishijima, Kazuyoshi
The present paper aims at enhancing a solution approach proposed by Anders & Nishijima (2011) to real-time decision problems in civil engineering. The approach takes basis in the Least Squares Monte Carlo method (LSM) originally proposed by Longstaff & Schwartz (2001) for computing American option...... the improvement of the computational efficiency is to “best utilize” the least squares method; i.e. least squares method is applied for estimating the expected utility for terminal decisions, conditional on realizations of underlying random phenomena at respective times in a parametric way. The implementation...
Multilevel solvers of first-order system least-squares for Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
Least-squares methods involving the H{sup -1} inner product
Energy Technology Data Exchange (ETDEWEB)
Pasciak, J.
1996-12-31
Least-squares methods are being shown to be an effective technique for the solution of elliptic boundary value problems. However, the methods differ depending on the norms in which they are formulated. For certain problems, it is much more natural to consider least-squares functionals involving the H{sup -1} norm. Such norms give rise to improved convergence estimates and better approximation to problems with low regularity solutions. In addition, fewer new variables need to be added and less stringent boundary conditions need to be imposed. In this talk, I will describe some recent developments involving least-squares methods utilizing the H{sup -1} inner product.
Dutta, Gaurav
2013-08-20
Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.
8th International Conference on Partial Least Squares and Related Methods
Vinzi, Vincenzo; Russolillo, Giorgio; Saporta, Gilbert; Trinchera, Laura
2016-01-01
This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics ...
Borodachev, S. M.
2016-06-01
The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.
Global Convergence of Adaptive Generalized Predictive Controller Based on Least Squares Algorithm
Institute of Scientific and Technical Information of China (English)
张兴会; 陈增强; 袁著祉
2003-01-01
Some papers on stochastic adaptive control schemes have established convergence algorithm using a leastsquares parameters. With the popular application of GPC, global convergence has become a key problem in automatic control theory. However, now global convergence of GPC has not been established for algorithms in computing a least squares iteration. A generalized model of adaptive generalized predictive control is presented. The global convergebce is also given on the basis of estimating the parameters of GPC by least squares algorithm.
ON STABLE PERTURBATIONS OF THE STIFFLY WEIGHTED PSEUDOINVERSE AND WEIGHTED LEAST SQUARES PROBLEM
Institute of Scientific and Technical Information of China (English)
Mu-sheng Wei
2005-01-01
In this paper we study perturbations of the stiffly weighted pseudoinverse (W1/2 A)+W1/2 and the related stiffly weighted least squares problem, where both the matrices A and W are given with W positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices (^)A = A+δA satisfy several row rank preserving conditions.
Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs
Energy Technology Data Exchange (ETDEWEB)
Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu
2017-01-15
This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.
Institute of Scientific and Technical Information of China (English)
ZHANG Liqing; WU Xiaohua
2005-01-01
The computer auxiliary partial least squares is introduced to simultaneously determine the contents of Deoxyschizandin, Schisandrin, γ- Schisandrin in the extracted solution of wuweizi. Regression analysis of the experimental results shows that the average recovery of each component is all in the range from 98.9% to 110.3% ,which means the partial least squares regression spectrophotometry can circumvent the overlapping of absorption spectrums of multi-components, so that satisfactory results can be obtained without any sample pre-separation.
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue (陶华学); GUO Jin-yun (郭金运)
2003-01-01
Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non-random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub-problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.
Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang
2016-03-01
An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS.
Directory of Open Access Journals (Sweden)
Jiao Long
2016-01-01
Full Text Available The application of interval partial least squares (IPLS and moving window partial least squares (MWPLS to the enantiomeric analysis of tryptophan (Trp was investigated. A UV-Vis spectroscopy method for determining the enantiomeric composition of Trp was developed. The calibration model was built by using partial least squares (PLS, IPLS and MWPLS respectively. Leave-one-out cross validation and external test validation were used to assess the prediction performance of the established models. The validation result demonstrates the established full-spectrum PLS model is impractical for quantifying the relationship between the spectral data and enantiomeric composition of L-Trp. On the contrary, the developed IPLS and MWPLS model are both practicable for modeling this relationship. For the IPLS model, the root mean square relative error (RMSRE of external test validation and leave-one-out cross validation is 4.03 and 6.50 respectively. For the MWPLS model, the RMSRE of external test validation and leave-one-out cross validation is 2.93 and 4.73 respectively. Obviously, the prediction accuracy of the MWPLS model is higher than that of the IPLS model. It is demonstrated UV-Vis spectroscopy combined with MWPLS is a commendable method for determining the enantiomeric composition of Trp. MWPLS is superior to IPLS for selecting spectral region in UV-Vis spectroscopy analysis.
Comparison of Kriging and Moving Least Square Methods to Change the Geometry of Human Body Models.
Jolivet, Erwan; Lafon, Yoann; Petit, Philippe; Beillas, Philippe
2015-11-01
Finite Element Human Body Models (HBM) have become powerful tools to study the response to impact. However, they are typically only developed for a limited number of sizes and ages. Various approaches driven by control points have been reported in the literature for the non-linear scaling of these HBM into models with different geometrical characteristics. The purpose of this study is to compare the performances of commonly used control points based interpolation methods in different usage scenarios. Performance metrics include the respect of target, the mesh quality and the runability. For this study, the Kriging and Moving Least square interpolation approaches were compared in three test cases. The first two cases correspond to changes of anthropometric dimensions of (1) a child model (from 6 to 1.5 years old) and (2) the GHBMC M50 model (Global Human Body Models Consortium, from 50th to 5th percentile female). For the third case, the GHBMC M50 ribcage was scaled to match the rib cage geometry derived from a CT-scan. In the first two test cases, all tested methods provided similar shapes with acceptable results in terms of time needed for the deformation (a few minutes at most), overall respect of the targets, element quality distribution and time step for explicit simulation. The personalization of rib cage proved to be much more challenging. None of the methods tested provided fully satisfactory results at the level of the rib trajectory and section. There were corrugated local deformations unless using a smooth regression through relaxation. Overall, the results highlight the importance of the target definition over the interpolation method.
Directory of Open Access Journals (Sweden)
Man Zhu
2017-03-01
Full Text Available Determination of ship maneuvering models is a tough task of ship maneuverability prediction. Among several prime approaches of estimating ship maneuvering models, system identification combined with the full-scale or free- running model test is preferred. In this contribution, real-time system identification programs using recursive identification method, such as the recursive least square method (RLS, are exerted for on-line identification of ship maneuvering models. However, this method seriously depends on the objects of study and initial values of identified parameters. To overcome this, an intelligent technology, i.e., support vector machines (SVM, is firstly used to estimate initial values of the identified parameters with finite samples. As real measured motion data of the Mariner class ship always involve noise from sensors and external disturbances, the zigzag simulation test data include a substantial quantity of Gaussian white noise. Wavelet method and empirical mode decomposition (EMD are used to filter the data corrupted by noise, respectively. The choice of the sample number for SVM to decide initial values of identified parameters is extensively discussed and analyzed. With de-noised motion data as input-output training samples, parameters of ship maneuvering models are estimated using RLS and SVM-RLS, respectively. The comparison between identification results and true values of parameters demonstrates that both the identified ship maneuvering models from RLS and SVM-RLS have reasonable agreements with simulated motions of the ship, and the increment of the sample for SVM positively affects the identification results. Furthermore, SVM-RLS using data de-noised by EMD shows the highest accuracy and best convergence.
The possibilities of least-squares migration of internally scattered seismic energy
Aldawood, Ali
2015-05-26
Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.
A Linear-correction Least-squares Approach for Geolocation Using FDOA Measurements Only
Institute of Scientific and Technical Information of China (English)
LI Jinzhou; GUO Fucheng; JIANG Wenli
2012-01-01
A linear-correction least-squares(LCLS) estimation procedure is proposed for geolocation using frequency difference of arrival(FDOA) measurements only.We first analyze the measurements of FDOA,and further derive the Cramér-Rao lower bound(CRLB) of geolocation using FDOA measurements.For the localization model is a nonlinear least squares(LS) estimator with a nonlinear constrained,a linearizing method is used to convert the model to a linear least squares estimator with a nonlinear constrained.The Gauss-Newton iteration method is developed to conquer the source localization problem.From the analysis of solving Lagrange multiplier,the algorithm is a generalization of linear-correction least squares estimation procedure under the condition of geolocation using FDOA measurements only.The algorithm is compared with common least squares estimation.Comparisons of their estimation accuracy and the CRLB are made,and the proposed method attains the CRLB.Simulation resuits are included to corroborate the theoretical development.
A note on implementation of decaying product correlation structures for quasi-least squares.
Shults, Justine; Guerra, Matthew W
2014-08-30
This note implements an unstructured decaying product matrix via the quasi-least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations. The structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix. It is straightforward to show that the quasi-least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure. Furthermore, subject to conditions that are easily checked, the quasi-least squares estimators are valid for longitudinal Bernoulli data. We demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable.
Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS
Directory of Open Access Journals (Sweden)
Ade Widyaningsih
2014-06-01
Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.
ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS
Institute of Scientific and Technical Information of China (English)
钟宝江
2002-01-01
The Galerkin and least-squares methods are two classes of the most popular Krylovsubspace methOds for solving large linear systems of equations. Unfortunately, both the methodsmay suffer from serious breakdowns of the same type: In a breakdown situation the Galerkinmethod is unable to calculate an approximate solution, while the least-squares method, althoughdoes not really break down, is unsucessful in reducing the norm of its residual. In this paper wefrst establish a unified theorem which gives a relationship between breakdowns in the two meth-ods. We further illustrate theoretically and experimentally that if the coefficient matrix of alienar system is of high defectiveness with the associated eigenvalues less than 1, then the restart-ed Galerkin and least-squares methods will be in great risks of complete breakdowns. It appearsthat our findings may help to understand phenomena observed practically and to derive treat-ments for breakdowns of this type.
ELASTO－PLASTICITY ANALYSIS BASED ON COLLOCATION WITH THE MOVING LEAST SQUARE METHOD
Institute of Scientific and Technical Information of China (English)
SongKangzu; ZhangXiong; LuMiugwau
2003-01-01
A meshless approach based on the moving least square method is developed for elasto-plasticity analysis, in which the incremental formulation is used. In this approach, the displacement shape functions are constructed by using the moving least square approximation, and the discrete governing equations for elasto-plastic material are constructed with the direct collocation method. The boundary conditions are also imposed by collocation. The method established is a truly meshless one, as it does not need any mesh, either for the purpose of interpolation of the solution variables, or for the purpose of construction of the discrete equations. It is simply formulated and very efficient, and no post-processing procedure is required to compute the derivatives of the unknown variables, since the solution from this method based on the moving least square approximation is already smooth enough. Numerical examples are given to verify the accuracy of the meshless method proposed for elasto-rdasticity analysis.
Meshless Least-Squares Method for Solving the Steady-State Heat Conduction Equation
Institute of Scientific and Technical Information of China (English)
LIU Yan; ZHANG Xiong; LU Mingwan
2005-01-01
The meshless weighted least-squares (MWLS) method is a pure meshless method that combines the moving least-squares approximation scheme and least-square discretization. Previous studies of the MWLS method for elastostatics and wave propagation problems have shown that the MWLS method possesses several advantages, such as high accuracy, high convergence rate, good stability, and high computational efficiency. In this paper, the MWLS method is extended to heat conduction problems. The MWLS computational parameters are chosen based on a thorough numerical study of 1-dimensional problems. Several 2-dimensional examples show that the MWLS method is much faster than the element free Galerkin method (EFGM), while the accuracy of the MWLS method is close to, or even better than the EFGM. These numerical results demonstrate that the MWLS method has good potential for numerical analyses of heat transfer problems.
On the equivalence of Kalman filtering and least-squares estimation
Mysen, E.
2016-07-01
The Kalman filter is derived directly from the least-squares estimator, and generalized to accommodate stochastic processes with time variable memory. To complete the link between least-squares estimation and Kalman filtering of first-order Markov processes, a recursive algorithm is presented for the computation of the off-diagonal elements of the a posteriori least-squares error covariance. As a result of the algebraic equivalence of the two estimators, both approaches can fully benefit from the advantages implied by their individual perspectives. In particular, it is shown how Kalman filter solutions can be integrated into the normal equation formalism that is used for intra- and inter-technique combination of space geodetic data.
On the equivalence of Kalman filtering and least-squares estimation
Mysen, E.
2017-01-01
The Kalman filter is derived directly from the least-squares estimator, and generalized to accommodate stochastic processes with time variable memory. To complete the link between least-squares estimation and Kalman filtering of first-order Markov processes, a recursive algorithm is presented for the computation of the off-diagonal elements of the a posteriori least-squares error covariance. As a result of the algebraic equivalence of the two estimators, both approaches can fully benefit from the advantages implied by their individual perspectives. In particular, it is shown how Kalman filter solutions can be integrated into the normal equation formalism that is used for intra- and inter-technique combination of space geodetic data.
Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection
Huang, Yunsong
2013-09-01
Multisource Least-Squares Migration (LSM) of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. But for the marine acquisition geometry this approach faces the challenge of erroneous misfit due to the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modeling method. To tackle this mismatch problem, I present a frequency selection strategy with LSM of supergathers. The key idea is, at each LSM iteration, to assign a unique frequency band to each shot gather, so that the spectral overlap among those shots—and therefore their crosstallk—is zero. Consequently, each receiver can unambiguously identify and then discount the superfluous sources—those that are not associated with the receiver in marine acquisition. To compare with standard migration, I apply the proposed method to 2D SEG/EAGE salt model and obtain better resolved images computed at about 1/8 the cost; results for 3D SEG/EAGE salt model, with Ocean Bottom Seismometer (OBS) survey, show a speedup of 40×. This strategy is next extended to multisource Full Waveform Inversion (FWI) of supergathers for marine streamer data, with the same advantages of computational efficiency and storage savings. In the Finite-Difference Time-Domain (FDTD) method, to mitigate spectral leakage due to delayed onsets of sine waves detected at receivers, I double the simulation time and retain only the second half of the simulated records. To compare with standard FWI, I apply the proposed method to 2D velocity model of SEG/EAGE salt and to Gulf Of Mexico (GOM) field data, and obtain a speedup of about 4× and 8×. Formulas are then derived for the resolution limits of various constituent wavepaths pertaining to FWI: diving waves, primary reflections, diffractions, and multiple reflections. They suggest that inverting multiples can provide some low and intermediate
Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach
Ulbrich, N.; Volden, T.
2017-01-01
A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.
Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression
Verdoolaege, G.; Shabbir, A.; Hornung, G.
2016-11-01
Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.
Analysis of total least squares in estimating the parameters of a mortar trajectory
Energy Technology Data Exchange (ETDEWEB)
Lau, D.L.; Ng, L.C.
1994-12-01
Least Squares (LS) is a method of curve fitting used with the assumption that error exists in the observation vector. The method of Total Least Squares (TLS) is more useful in cases where there is error in the data matrix as well as the observation vector. This paper describes work done in comparing the LS and TLS results for parameter estimation of a mortar trajectory based on a time series of angular observations. To improve the results, we investigated several derivations of the LS and TLS methods, and early findings show TLS provided slightly, 10%, improved results over the LS method.
Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares
Pilipchuk, V N
2011-01-01
A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of the controller must be inversely related to insure that vanishing the time step has little effect on the results. The algorithm is illustrated on two linearly coupled Duffing oscillators near the 1:1 internal resonance. In particular, it is shown that varying the dissipation ratio of one of the two oscillators can significantly suppress the nonlinear beat phenomenon.
Influence of the least-squares phase on optical vortices in strongly scintillated beams
CSIR Research Space (South Africa)
Chen, M
2009-06-01
Full Text Available of dipole annihilations in a random wave fleld is balanced by the rate of dipole creations. This is reminiscent of a plasma in equilibrium where the rate of ionization is balanced by the rate of recombination. For this reason it is reasonable to model a.... A least-squares phase remover is put directly behind the system aperture. This least-squares phase remover is just a conventional adaptive optics system. It measures the incident wavefront with a wavefront sensor such as a Shack...
Simulation of Foam Divot Weight on External Tank Utilizing Least Squares and Neural Network Methods
Chamis, Christos C.; Coroneos, Rula M.
2007-01-01
Simulation of divot weight in the insulating foam, associated with the external tank of the U.S. space shuttle, has been evaluated using least squares and neural network concepts. The simulation required models based on fundamental considerations that can be used to predict under what conditions voids form, the size of the voids, and subsequent divot ejection mechanisms. The quadratic neural networks were found to be satisfactory for the simulation of foam divot weight in various tests associated with the external tank. Both linear least squares method and the nonlinear neural network predicted identical results.
A New Neural Network for Solving a Class of Constrained Least Square Problems
Institute of Scientific and Technical Information of China (English)
YE Dazhen; XIA Youshen; WU Xinyu
2001-01-01
A new neural network for solvinga class of constrained least square problems is pre-sented. The network is shown to be completely stableand globally convergent to the exact solutions to theconstrained least square problem. In contrast to theneural network proposed in the Ref.[1], our new neu-ral network has the following advantages in two ma-jor aspects. First, the convergent region of this newnetwork is the whole space Rn. Second, in hardwareimplementations this new network does not need theexpensive analogue multiplier for variables.
Hierarchical Least Squares Identification and Its Convergence for Large Scale Multivariable Systems
Institute of Scientific and Technical Information of China (English)
丁锋; 丁韬
2002-01-01
The recursive least squares identification algorithm (RLS) for large scale multivariable systems requires a large amount of calculations, therefore, the RLS algorithm is difficult to implement on a computer. The computational load of estimation algorithms can be reduced using the hierarchical least squares identification algorithm (HLS) for large scale multivariable systems. The convergence analysis using the Martingale Convergence Theorem indicates that the parameter estimation error (PEE) given by the HLS algorithm is uniformly bounded without a persistent excitation signal and that the PEE consistently converges to zero for the persistent excitation condition. The HLS algorithm has a much lower computational load than the RLS algorithm.
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Varneskov, Rasmus T.
band least squares (MBLS) estimator uses sample dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing...... the cointegration strength and testing MBLS against the existing narrow band least squares estimator are developed. Finally, the asymptotic framework for the MBLS estimator is used to provide new perspectives on volatility factors in an empirical application to long-span realized variance series for S&P 500...
A Least-Squares Solution to Nonlinear Steady-State Multi-Dimensional IHCP
Institute of Scientific and Technical Information of China (English)
无
1996-01-01
In this paper,the least-squares method is used to solve the Inverse Heat Conduction Probles(IHCP) to determine the space-wise variation of the unknown boundary condition on the inner surface of a helically coied tube with fluid flow inside,electrical heating and insulation outside.The sensitivity coefficient is analyzed to give a rational distribution of the thermocouples.The results demonstrate that the method effectively extracts information about the unknown boundary condition for the heat conduction problem from the experimental measurements.The results also show that the least-squares method conerges very quickly.
Institute of Scientific and Technical Information of China (English)
YUEYuncan; QIANJixin
2002-01-01
Based on the idea of the set-membership identification,a modified recursive least squares algorithm with variable gain, variable forgetting factor and resetting is presented.The concept of the error tolerance level is proposed.The selection criteria of the error tolerance level are also given according to the min-max principle.The algorithm is particularly suitable for tracing time-varying systems and is similar in computational complexity to the standard recursive least squares algorithm.The superior performance of the algorithm is verified via simulation studies on a dynamic fermentation process.
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue; GUO Jin-yun
2005-01-01
The unknown parameter's variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now,which didn't appear in the internal and external referencing documents. The unknown parameter's variance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source,multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.
ALGEBRAIC OPERATION OF SPECIAL MATRICES RELATED TO METHOD OF LEAST SQUARES
Institute of Scientific and Technical Information of China (English)
XuFuhua
2003-01-01
The follwing situation in using the method of least squares to solve problems often occurs.After m experiments completed and a solution of least squares obtained,the(m+1)-th experiment is made further in order to improve the results.A method of algebraic operation of special matrices involed in the problem is given is this paper for obtaining a new solution for the m+1 experiments based upon the old solution for the primary m experiments .This method is valid for more general matrices.
Institute of Scientific and Technical Information of China (English)
Ge-mai Chen; Jin-hong You
2005-01-01
Consider a repeated measurement partially linear regression model with an unknown vector pasemiparametric generalized least squares estimator (SGLSE) ofβ, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE.These results are generalizations of those in [2] to the case of semiparametric regressions.
Least square neural network model of the crude oil blending process.
Rubio, José de Jesús
2016-06-01
In this paper, the recursive least square algorithm is designed for the big data learning of a feedforward neural network. The proposed method as the combination of the recursive least square and feedforward neural network obtains four advantages over the alone algorithms: it requires less number of regressors, it is fast, it has the learning ability, and it is more compact. Stability, convergence, boundedness of parameters, and local minimum avoidance of the proposed technique are guaranteed. The introduced strategy is applied for the modeling of the crude oil blending process.
Ling, Zhao; Yeling, Wang; Guijun, Hu; Yunpeng, Cui; Jian, Shi; Li, Li
2013-07-01
Recursive least squares constant modulus algorithm based on QR decomposition (QR-RLS-CMA) is first proposed as the polarization demultiplexing method. We compare its performance with the stochastic gradient descent constant modulus algorithm (SGD-CMA) and the recursive least squares constant modulus algorithm (RLS-CMA) in a polarization-division-multiplexing system with coherent detection. It is demonstrated that QR-RLS-CMA is an efficient demultiplexing algorithm which can avoid the problem of step-length choice in SGD-CMA. Meanwhile, it also has better symbol error rate (SER) performance and more stable convergence property.
Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations
Directory of Open Access Journals (Sweden)
Hongcai Yin
2014-01-01
Full Text Available By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations AX+YB=C and DX+YE=F in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation AXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm.
Constrained total least squares algorithm for passive location based on bearing-only measurements
Institute of Scientific and Technical Information of China (English)
WANG Ding; ZHANG Li; WU Ying
2007-01-01
The constrained total least squares algorithm for the passive location is presented based on the bearing-only measurements in this paper. By this algorithm the non-linear measurement equations are firstly transformed into linear equations and the effect of the measurement noise on the linear equation coefficients is analyzed,therefore the problem of the passive location can be considered as the problem of constrained total least squares, then the problem is changed into the optimized question without restraint which can be solved by the Newton algorithm, and finally the analysis of the location accuracy is given. The simulation results prove that the new algorithm is effective and practicable.
Institute of Scientific and Technical Information of China (English)
WANG Ding; ZHANG Li; WU Ying
2009-01-01
Based on the constrained total least squares (CTLS) passive location algorithm with bearing-only measurements, in this paper, the same passive location problem is transformed into the structured total least squares (STLS) problem. The solution of the STLS problem for passive location can be obtained using the inverse iteration method. It also expatiates that both the STLS algorithm and the CTLS algorithm have the same location mean squares error under certain condition. Finally, the article presents a kind of location and tracking algorithm for moving target by combining STLS location algorithm with Kalman filter (KF). The efficiency and superiority of the proposed algorithms can be confirmed by computer simulation results.
Efectivity of Additive Spline for Partial Least Square Method in Regression Model Estimation
Directory of Open Access Journals (Sweden)
Ahmad Bilfarsah
2005-04-01
Full Text Available Additive Spline of Partial Least Square method (ASPL as one generalization of Partial Least Square (PLS method. ASPLS method can be acommodation to non linear and multicollinearity case of predictor variables. As a principle, The ASPLS method approach is cahracterized by two idea. The first is to used parametric transformations of predictors by spline function; the second is to make ASPLS components mutually uncorrelated, to preserve properties of the linear PLS components. The performance of ASPLS compared with other PLS method is illustrated with the fisher economic application especially the tuna fish production.
Directory of Open Access Journals (Sweden)
Pudji Ismartini
2010-08-01
Full Text Available One of the major problem facing the data modelling at social area is multicollinearity. Multicollinearity can have significant impact on the quality and stability of the fitted regression model. Common classical regression technique by using Least Squares estimate is highly sensitive to multicollinearity problem. In such a problem area, Partial Least Squares Regression (PLSR is a useful and flexible tool for statistical model building; however, PLSR can only yields point estimations. This paper will construct the interval estimations for PLSR regression parameters by implementing Jackknife technique to poverty data. A SAS macro programme is developed to obtain the Jackknife interval estimator for PLSR.
A LEAST-SQUARES FINITE ELEMENT METHOD FOR LARGE EDDY SIMULATION OF TURBULENT FLOWS. (R825200)
The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...
van Ophem, S.; Berkhoff, Arthur P.
2016-01-01
For broadband active noise control applications with a rapidly changing primary path, it is desirable to find algorithms with a rapid convergence, a fast tracking performance, and a low computational cost. Recently, a promising algorithm has been presented, called the fast-array Kalman filter, which
Mixing subalgebras of finite von Neumann algebras
Cameron, Jan; Mukherjee, Kunal
2010-01-01
Jolissaint and Stalder introduced the definitions of mixing and weak mixing for von Neumann subalgebras of finite von Neumann algebras. In this paper, we study various algebraic and analytical properties of mixing and weakly mixing von Neumann subalgebras. We prove some basic results about mixing inclusions of von Neumann algebras and establish a connection between mixing properties and normalizers of von Neumann subalgebras. The special case of mixing subalgebras arising from inclusions of group von Neumann algebras finds applications to ergodic theory. For a finite von Neumann algebra $M$ and von Neumann subalgebras $A$, $B$ of $M$, we introduce a notion of weak mixing of $B\\subseteq M$ relative to $A$. If $B$ is abelian and $A\\subset B$, we show that weak mixing of $B \\subset M$ relative to $A$ is equivalent to the following property: if $x\\in M$ and $xAx^*\\subset B$ then $x\\in B$. In the general case, we show that weak mixing of $B\\subset M$ relative to $A$ is equivalent to the following property: if $x\\i...
Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J
2006-09-01
A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (
Representing Topography with Second-Degree Bivariate Polynomial Functions Fitted by Least Squares.
Neuman, Arthur Edward
1987-01-01
There is a need for abstracting topography other than for mapping purposes. The method employed should be simple and available to non-specialists, thereby ruling out spline representations. Generalizing from univariate first-degree least squares and from multiple regression, this article introduces bivariate polynomial functions fitted by least…
Fully Modified Narrow-Band Least Squares Estimation of Weak Fractional Cointegration
DEFF Research Database (Denmark)
Nielsen, Morten Ørregaard; Frederiksen, Per
application recently, especially in financial economics. Previous research on this model has considered a semiparametric narrow-band least squares (NBLS) estimator in the frequency domain, but in the stationary case its asymptotic distribution has been derived only under a condition of non-coherence between...
A Progress Report on Numerical Solutions of Least Squares Adjustment in GNU Project Gama
Directory of Open Access Journals (Sweden)
A. Čepek
2005-01-01
Full Text Available GNU project Gama for adjustment of geodetic networks is presented. Numerical solution of Least Squares Adjustment in the project is based on Singular Value Decomposition (SVD and General Orthogonalization Algorithm (GSO. Both algorithms enable solution of singular systems resulting from adjustment of free geodetic networks.
Least-squares spectral element method applied to the Euler equations
Gerritsma, M.I.; Bas, R. van der; De Maerschalck, B.; Koren, B.; Deconinck, H.
2008-01-01
This paper describes the application of the least-squares spectral element method to compressible flow problems. Special attention is paid to the imposition of the weak boundary conditions along curved walls and the influence of the time step on the position and resolution of shocks. The method is d
Harmonic tidal analysis at a few stations using the least squares method
Digital Repository Service at National Institute of Oceanography (India)
Fernandes, A.A; Das, V.K.; Bahulayan, N.
Using the least squares method, harmonic analysis has been performed on hourly water level records of 29 days at several stations depicting different types of non-tidal noise. For a tidal record at Mormugao, which was free from storm surges (low...
An unstructured parallel least-squares spectral element solver for incompressible flow problems
Nool, M.; Proot, M.M.J.
2003-01-01
The parallelization of the least-squares spectral element formulation of the Stokes problem has recently been discussed for incompressible flow problems on structured grids. In the present work, the extension to unstructured grids is discussed. It will be shown that, to obtain an efficient and scala
Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition
Baur, O.; Austen, G.; Kusche, J.
2007-01-01
We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly,
APPLICATION OF PARTIAL LEAST SQUARES REGRESSION FOR AUDIO-VISUAL SPEECH PROCESSING AND MODELING
Directory of Open Access Journals (Sweden)
A. L. Oleinik
2015-09-01
Full Text Available Subject of Research. The paper deals with the problem of lip region image reconstruction from speech signal by means of Partial Least Squares regression. Such problems arise in connection with development of audio-visual speech processing methods. Audio-visual speech consists of acoustic and visual components (called modalities. Applications of audio-visual speech processing methods include joint modeling of voice and lips’ movement dynamics, synchronization of audio and video streams, emotion recognition, liveness detection. Method. Partial Least Squares regression was applied to solve the posed problem. This method extracts components of initial data with high covariance. These components are used to build regression model. Advantage of this approach lies in the possibility of achieving two goals: identification of latent interrelations between initial data components (e.g. speech signal and lip region image and approximation of initial data component as a function of another one. Main Results. Experimental research on reconstruction of lip region images from speech signal was carried out on VidTIMIT audio-visual speech database. Results of the experiment showed that Partial Least Squares regression is capable of solving reconstruction problem. Practical Significance. Obtained findings give the possibility to assert that Partial Least Squares regression is successfully applicable for solution of vast variety of audio-visual speech processing problems: from synchronization of audio and video streams to liveness detection.
How to handle colored observation noise in large least-squares problems
Klees, R.; Ditmar, P.; Broersen, P.
2003-01-01
An approach to handling colored observation noise in large least-squares (LS) problems is presented. The handling of colored noise is reduced to the problem of solving a Toeplitz system of linear equations. The colored noise is represented as an auto regressive moving-average (ARMA) process. Stabili
DEFF Research Database (Denmark)
Nolte, Ingmar; Voev, Valeri
The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise...
Gauss’s, Cholesky’s and Banachiewicz’s Contributions to Least Squares
DEFF Research Database (Denmark)
Gustavson, Fred G.; Wasniewski, Jerzy
This paper describes historically Gauss’s contributions to the area of Least Squares. Also mentioned are Cholesky’s and Banachiewicz’s contributions to linear algebra. The material given is backup information to a Tutorial given at PPAM 2011 to honor Cholesky on the hundred anniversary of his...
Huang, Jie-Tsuen; Hsieh, Hui-Hsien
2011-01-01
The purpose of this study was to investigate the contributions of socioeconomic status (SES) in predicting social cognitive career theory (SCCT) factors. Data were collected from 738 college students in Taiwan. The results of the partial least squares (PLS) analyses indicated that SES significantly predicted career decision self-efficacy (CDSE);…
A comparison of least-squares and Bayesian minimum risk edge parameter estimation
Mulder, Nanno J.; Abkar, Ali A.
1999-01-01
The problem considered here is to compare two methods for finding a common boundary between two objects with two unknown geometric parameters, such as edge position and edge orientation. We compare two model-based approaches: the least squares and the minimum Bayesian risk method. An expression is d
Sarstedt, Marko; Henseler, Jörg; Ringle, Christian M.
2011-01-01
Purpose – Partial least squares (PLS) path modeling has become a pivotal empirical research method in international marketing. Owing to group comparisons' important role in research on international marketing, we provide researchers with recommendations on how to conduct multigroup analyses in PLS p
Guo, Shiguang; Zhang, Bo; Wang, Qing; Cabrales-Vargas, Alejandro; Marfurt, Kurt J.
2016-08-01
Conventional Kirchhoff migration often suffers from artifacts such as aliasing and acquisition footprint, which come from sub-optimal seismic acquisition. The footprint can mask faults and fractures, while aliased noise can focus into false coherent events which affect interpretation and contaminate amplitude variation with offset, amplitude variation with azimuth and elastic inversion. Preconditioned least-squares migration minimizes these artifacts. We implement least-squares migration by minimizing the difference between the original data and the modeled demigrated data using an iterative conjugate gradient scheme. Unpreconditioned least-squares migration better estimates the subsurface amplitude, but does not suppress aliasing. In this work, we precondition the results by applying a 3D prestack structure-oriented LUM (lower-upper-middle) filter to each common offset and common azimuth gather at each iteration. The preconditioning algorithm not only suppresses aliasing of both signal and noise, but also improves the convergence rate. We apply the new preconditioned least-squares migration to the Marmousi model and demonstrate how it can improve the seismic image compared with conventional migration, and then apply it to one survey acquired over a new resource play in the Mid-Continent, USA. The acquisition footprint from the targets is attenuated and the signal to noise ratio is enhanced. To demonstrate the impact on interpretation, we generate a suite of seismic attributes to image the Mississippian limestone, and show that the karst-enhanced fractures in the Mississippian limestone can be better illuminated.
Robust Mean and Covariance Structure Analysis through Iteratively Reweighted Least Squares.
Yuan, Ke-Hai; Bentler, Peter M.
2000-01-01
Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)
Least-Squares Approaches for the Time-Dependent Maxwell Equations
Energy Technology Data Exchange (ETDEWEB)
Zhiquiang, C; Jones, J
2001-12-01
When the author was at CASC in LLNL during the period between July and December of last year, he was working on two research topics: (1) least-squares approaches for elasticity and Maxwell equations and (2) high-accuracy approximations for non-smooth problems.
Superresolution of 3-D computational integral imaging based on moving least square method.
Kim, Hyein; Lee, Sukho; Ryu, Taekyung; Yoon, Jungho
2014-11-17
In this paper, we propose an edge directive moving least square (ED-MLS) based superresolution method for computational integral imaging reconstruction(CIIR). Due to the low resolution of the elemental images and the alignment error of the microlenses, it is not easy to obtain an accurate registration result in integral imaging, which makes it difficult to apply superresolution to the CIIR application. To overcome this problem, we propose the edge directive moving least square (ED-MLS) based superresolution method which utilizes the properties of the moving least square. The proposed ED-MLS based superresolution takes the direction of the edge into account in the moving least square reconstruction to deal with the abrupt brightness changes in the edge regions, and is less sensitive to the registration error. Furthermore, we propose a framework which shows how the data have to be collected for the superresolution problem in the CIIR application. Experimental results verify that the resolution of the elemental images is enhanced, and that a high resolution reconstructed 3-D image can be obtained with the proposed method.
Use of correspondence analysis partial least squares on linear and unimodal data
DEFF Research Database (Denmark)
Frisvad, Jens C.; Bergsøe, Merete Norsker
1996-01-01
Correspondence analysis partial least squares (CA-PLS) has been compared with PLS conceming classification and prediction of unimodal growth temperature data and an example using infrared (IR) spectroscopy for predicting amounts of chemicals in mixtures. CA-PLS was very effective for ordinating...
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2002-01-01
Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.
A Comparison of Mean Phase Difference and Generalized Least Squares for Analyzing Single-Case Data
Manolov, Rumen; Solanas, Antonio
2013-01-01
The present study focuses on single-case data analysis specifically on two procedures for quantifying differences between baseline and treatment measurements. The first technique tested is based on generalized least square regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The…
Using Technology to Optimize and Generalize: The Least-Squares Line
Burke, Maurice J.; Hodgson, Ted R.
2007-01-01
With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes. (Contains 4…
Rocconi, Louis M.
2013-01-01
This study examined the differing conclusions one may come to depending upon the type of analysis chosen, hierarchical linear modeling or ordinary least squares (OLS) regression. To illustrate this point, this study examined the influences of seniors' self-reported critical thinking abilities three ways: (1) an OLS regression with the student…
Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions
Institute of Scientific and Technical Information of China (English)
ZHU Meng-Hua; LIU Liang-Gang; QI Dong-Xu; YOU Zhong; XU Ao-Ao
2009-01-01
In this paper,the least square fitting method with the cubic B-spline basis hmctioas is derived to reduce the influence of statistical fluctuations in the gamma ray spectra.The derived procedure is simple and automatic.The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.
Vargas, M.; Crossa, J.; Eeuwijk, van F.A.; Ramirez, M.E.; Sayre, K.
1999-01-01
Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external environmental and/or cultivar variables for studying and interpreting genotype × environment interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only th
Risk Bounds for Regularized Least-Squares Algorithm with Operator-Value Kernels
2005-05-16
for regularized least-squares algorithm with operator-valued kernels Ernesto De Vito a Andrea Caponnetto b aDipartimento di Matematica , Università...0915, National Science Foundation (ITR/SYS) Contract No. IIS - 0112991, National Science Foundation (ITR) Contract No. IIS -0209289, National Science
Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes
Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)
2003-01-01
The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.
On Fits of Seasonal Data by the Ordinary Least Square Method
Rotundo, G; Herteli, C; Ileanu, B V
2016-01-01
Following Shimura et al. pioneering paper (1981) on "Geographical and secular changes in the seasonal distribution of births", much data has been reported by seasonal effects time series. We discuss how one can be misled in testing Linear Regression Models by an Ordinary Least Square method.
1985-05-01
first generated the errors and response variables. The errors, i, were produced using the Marsaglia and Tsang pseudo-normal ran- dom number algorithm...34Asymptotic properties of non-linear least squares estimators," The Annals of Mathematical Statistici, 40(2), pp. 633-643. Marsaglia , G., Tsang, W
Memory and computation reduction for least-square channel estimation of mobile OFDM systems
Xu, T.; Tang, Z.; Lu, H.; Leuken, R van
2012-01-01
Mobile OFDM refers to OFDM systems with fast moving transceivers, contrastive to traditional OFDM systems whose transceivers are stationary or have a low velocity. In this paper, we use Basis Expansion Models (BEM) to model the time-variation of channels, based on which two least-squares (LS) channe
Chkifa, Abdellah
2015-04-08
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R. Tempone, Found. Comput. Math. 14 (2014) 419–456], under suitable conditions that relate the number of samples with respect to the dimension of the polynomial space. Here “quasi-optimal” means that the accuracy of the least-squares approximation is comparable with that of the best approximation in the given polynomial space. In this paper, we discuss the quasi-optimality of the polynomial least-squares method in arbitrary dimension. Our analysis applies to any arbitrary multivariate polynomial space (including tensor product, total degree or hyperbolic crosses), under the minimal requirement that its associated index set is downward closed. The optimality criterion only involves the relation between the number of samples and the dimension of the polynomial space, independently of the anisotropic shape and of the number of variables. We extend our results to the approximation of Hilbert space-valued functions in order to apply them to the approximation of parametric and stochastic elliptic PDEs. As a particular case, we discuss “inclusion type” elliptic PDE models, and derive an exponential convergence estimate for the least-squares method. Numerical results confirm our estimate, yet pointing out a gap between the condition necessary to achieve optimality in the theory, and the condition that in practice yields the optimal convergence rate.
总体最小二乘解性质研究%RESEARCH ON PROPERTIES OF TOTAL LEAST SQUARES ESTIMATION
Institute of Scientific and Technical Information of China (English)
王乐洋
2012-01-01
通过理论推导,发现总体最小二乘解是最小二乘解的线性变换；当系数矩阵含有误差时最小二乘解是有偏的,而总体最小二乘解是无偏的；总体最小二乘解的条件数大于最小二乘解的条件数,总体最小二乘解更容易受到数据误差的影响.通过进一步推导给出了总体最小二乘与最小二乘在解、残差、单位权方差估值等方面的关系式.%Through theory derivation and proof, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation. When the coefficient matrix contains error,the least squares is biased. The total least squares estimation is unbiased. The condition number of the total least squares estimation is bigger than that of the least squares estimation, so the total least squares estimation is more easier to be affected by the data error than the least squares estimation. Through further derivation, the relation of solutions, residuals, unit weight variance estimations between the total least squares and the least squares are given.
Zhan, Xiaobin; Jiang, Shulan; Yang, Yili; Liang, Jian; Shi, Tielin; Li, Xiwen
2015-09-18
This paper proposes an ultrasonic measurement system based on least squares support vector machines (LS-SVM) for inline measurement of particle concentrations in multicomponent suspensions. Firstly, the ultrasonic signals are analyzed and processed, and the optimal feature subset that contributes to the best model performance is selected based on the importance of features. Secondly, the LS-SVM model is tuned, trained and tested with different feature subsets to obtain the optimal model. In addition, a comparison is made between the partial least square (PLS) model and the LS-SVM model. Finally, the optimal LS-SVM model with the optimal feature subset is applied to inline measurement of particle concentrations in the mixing process. The results show that the proposed method is reliable and accurate for inline measuring the particle concentrations in multicomponent suspensions and the measurement accuracy is sufficiently high for industrial application. Furthermore, the proposed method is applicable to the modeling of the nonlinear system dynamically and provides a feasible way to monitor industrial processes.
Energy Technology Data Exchange (ETDEWEB)
Vincent M. Laboure; Yaqi Wang; Mark D. DeHart
2016-05-01
In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.
L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing
Demetriou, I. C.
2006-04-01
Fortran 77 software is given for least squares smoothing to data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is also unknown of the optimization problem. A highly useful description of the constraints is that they follow from the assumption of initially increasing and subsequently decreasing rates of change, or vice versa, of the process considered. The underlying algorithm partitions the data into two disjoint sets of adjacent data and calculates the required fit by solving a strictly convex quadratic programming problem for each set. The piecewise linear interpolant to the fit is convex on the first set and concave on the other one. The partition into suitable sets is achieved by a finite iterative algorithm, which is made quite efficient because of the interactions of the quadratic programming problems on consecutive data. The algorithm obtains the solution by employing no more quadratic programming calculations over subranges of data than twice the number of the divided differences constraints. The quadratic programming technique makes use of active sets and takes advantage of a B-spline representation of the smoothed values that allows some efficient updating procedures. The entire code required to implement the method is 2920 Fortran lines. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes over subranges of data that is only proportional to the number of data. The results suggest that the package can be used for very large numbers of data values. Some examples with output are provided to help new users and exhibit certain features of the software. Important applications of the smoothing technique may be found in calculating a sigmoid approximation, which is a common topic in various contexts in applications in disciplines like physics, economics
Institute of Scientific and Technical Information of China (English)
Musheng Wei; Qiaohua Liu
2007-01-01
Recently,Wei in[18]proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable,if and only if the original and perturbed coefficient matrices A and A satisfy several row rank preservation conditions.According to these conditions,in this paper we show that in general,ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem.We then propose a row block modified Gram-Schmidt algorithm with column pivoting,and show that with appropriately chosen tolerance,this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices,and the computed QR factor R contains small roundoff error which is row stable.Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting.
A note on the total least squares problem for coplanar points
Energy Technology Data Exchange (ETDEWEB)
Lee, S.L.
1994-09-01
The Total Least Squares (TLS) fit to the points (x{sub k}, y{sub k}), k = 1, {hor_ellipsis}, n, minimizes the sum of the squares of the perpendicular distances from the points to the line. This sum is the TLS error, and minimizing its magnitude is appropriate if x{sub k} and y{sub k} are uncertain. A priori formulas for the TLS fit and TLS error to coplanar points were originally derived by Pearson, and they are expressed in terms of the mean, standard deviation and correlation coefficient of the data. In this note, these TLS formulas are derived in a more elementary fashion. The TLS fit is obtained via the ordinary least squares problem and the algebraic properties of complex numbers. The TLS error is formulated in terms of the triangle inequality for complex numbers.
Least Square Regression Method for Estimating Gas Concentration in an Electronic Nose System
Directory of Open Access Journals (Sweden)
Walaa Khalaf
2009-03-01
Full Text Available We describe an Electronic Nose (ENose system which is able to identify the type of analyte and to estimate its concentration. The system consists of seven sensors, five of them being gas sensors (supplied with different heater voltage values, the remainder being a temperature and a humidity sensor, respectively. To identify a new analyte sample and then to estimate its concentration, we use both some machine learning techniques and the least square regression principle. In fact, we apply two different training models; the first one is based on the Support Vector Machine (SVM approach and is aimed at teaching the system how to discriminate among different gases, while the second one uses the least squares regression approach to predict the concentration of each type of analyte.
Least Squares Ranking on Graphs, Hodge Laplacians, Time Optimality, and Iterative Methods
Hirani, Anil N; Watts, Seth
2010-01-01
Given a set of alternatives to be ranked and some pairwise comparison values, ranking can be posed as a least squares computation on a graph. This was first used by Leake for ranking football teams. The residual can be further analyzed to find inconsistencies in the given data, and this leads to a second least squares problem. This whole process was formulated recently by Jiang et al. as a Hodge decomposition of the edge values. Recently, Koutis et al., showed that linear systems involving symmetric diagonally dominant (SDD) matrices can be solved in time approaching optimality. By using Hodge 0-Laplacian and 2-Laplacian, we give various results on when the normal equations for ranking are SDD and when iterative Krylov methods should be used. We also give iteration bounds for conjugate gradient method for these problems.
Zheng, Jun; Shao, Xinyu; Gao, Liang; Jiang, Ping; Qiu, Haobo
2015-06-01
Engineering design, especially for complex engineering systems, is usually a time-consuming process involving computation-intensive computer-based simulation and analysis methods. A difference mapping method using least square support vector regression is developed in this work, as a special metamodelling methodology that includes variable-fidelity data, to replace the computationally expensive computer codes. A general difference mapping framework is proposed where a surrogate base is first created, then the approximation is gained by a mapping the difference between the base and the real high-fidelity response surface. The least square support vector regression is adopted to accomplish the mapping. Two different sampling strategies, nested and non-nested design of experiments, are conducted to explore their respective effects on modelling accuracy. Different sample sizes and three approximation performance measures of accuracy are considered.
Geodesic least squares regression for scaling studies in magnetic confinement fusion
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2015-01-13
In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.
A Least Square-Based Self-Adaptive Localization Method for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Baoguo Yu
2016-01-01
Full Text Available In the wireless sensor network (WSN localization methods based on Received Signal Strength Indicator (RSSI, it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.
Least square regression method for estimating gas concentration in an electronic nose system.
Khalaf, Walaa; Pace, Calogero; Gaudioso, Manlio
2009-01-01
We describe an Electronic Nose (ENose) system which is able to identify the type of analyte and to estimate its concentration. The system consists of seven sensors, five of them being gas sensors (supplied with different heater voltage values), the remainder being a temperature and a humidity sensor, respectively. To identify a new analyte sample and then to estimate its concentration, we use both some machine learning techniques and the least square regression principle. In fact, we apply two different training models; the first one is based on the Support Vector Machine (SVM) approach and is aimed at teaching the system how to discriminate among different gases, while the second one uses the least squares regression approach to predict the concentration of each type of analyte.
ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING Α-STABLE MOTIONS
Institute of Scientific and Technical Information of China (English)
Hu Yaozhong; Long Hongwei
2009-01-01
We study the problem of parameter estimation for mean-reverting α-stable motion, dXt= (a0- θ0Xt)dt + dZt, observed at discrete time instants.A least squares estimator is obtained and its asymptotics is discussed in the singular case (a0, θ0)=(0,0).If a0=0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodie case θ0 > 0.For the Ornstein-Uhlenbeck process, asymptoties of the least squares estimators for the singular case (θ0 = 0) and for ergodic case (θ0 > 0) are completely different.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A new robust on-line fault diagnosis method based on least squares estimate for nonlinear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of the DAS, this method firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation, then, based on the relationship between the state deviation and the faults in the difference equation and the relationship between the algebraic variable deviation and the faults in algebraic equation, it identifies the faults on-line through least squares estimate. This method can not only detect, isolate and identify faults for DAS, but also give the upper bound of the error of fault identification. The simulation results indicate that it can give satisfactory diagnostic results for both abrupt and incipient faults.
Malik, Bilal; Benaissa, Mohammed
2012-01-01
This paper proposes the use of locally weighted partial least square regression (LW-PLSR) as an alternative multivariate calibration method for the prediction of glucose concentration from NIR spectra. The efficiency of the proposed model is validated in experiments carried out in a non-controlled environment or sample conditions using mixtures composed of glucose, urea and triacetin. The collected data spans the spectral region from 2100 nm to 2400 nm with spectra resolution of 1 nm. The results show that the standard error of prediction (SEP) decreases to 23.85 mg/dL when using LW-PLSR in comparison to the SEP values of 49.40 mg/dL, and 27.56 mg/dL using Principal Component Regression (PCR) and Partial Least Square (PLS) regression respectively.
Method for exploiting bias in factor analysis using constrained alternating least squares algorithms
Keenan, Michael R.
2008-12-30
Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.
Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization
Transtrum, Mark K
2012-01-01
When minimizing a nonlinear least-squares function, the Levenberg-Marquardt algorithm can suffer from a slow convergence, particularly when it must navigate a narrow canyon en route to a best fit. On the other hand, when the least-squares function is very flat, the algorithm may easily become lost in parameter space. We introduce several improvements to the Levenberg-Marquardt algorithm in order to improve both its convergence speed and robustness to initial parameter guesses. We update the usual step to include a geodesic acceleration correction term, explore a systematic way of accepting uphill steps that may increase the residual sum of squares due to Umrigar and Nightingale, and employ the Broyden method to update the Jacobian matrix. We test these changes by comparing their performance on a number of test problems with standard implementations of the algorithm. We suggest that these two particular challenges, slow convergence and robustness to initial guesses, are complimentary problems. Schemes that imp...
Real-Time Adaptive Least-Squares Drag Minimization for Performance Adaptive Aeroelastic Wing
Ferrier, Yvonne L.; Nguyen, Nhan T.; Ting, Eric
2016-01-01
This paper contains a simulation study of a real-time adaptive least-squares drag minimization algorithm for an aeroelastic model of a flexible wing aircraft. The aircraft model is based on the NASA Generic Transport Model (GTM). The wing structures incorporate a novel aerodynamic control surface known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF). The drag minimization algorithm uses the Newton-Raphson method to find the optimal VCCTEF deflections for minimum drag in the context of an altitude-hold flight control mode at cruise conditions. The aerodynamic coefficient parameters used in this optimization method are identified in real-time using Recursive Least Squares (RLS). The results demonstrate the potential of the VCCTEF to improve aerodynamic efficiency for drag minimization for transport aircraft.
Least Orthogonal Distance Estimator and Total Least Square for Simultaneous Equation Models
Directory of Open Access Journals (Sweden)
Alessia Naccarato
2014-01-01
Full Text Available Least Orthogonal Distance Estimator (LODE of Simultaneous Equation Models’ structural parameters is based on minimizing the orthogonal distance between Reduced Form (RF and the Structural Form (SF parameters. In this work we propose a new version – with respect to Pieraccini and Naccarato (2008 – of Full Information (FI LODE based on decomposition of a new structure of the variance-covariance matrix using Singular Value Decomposition (SVD instead of Spectral Decomposition (SD. In this context Total Least Square is applied. A simulation experiment to compare the performances of the new version of FI LODE with respect to Three Stage Least Square (3SLS and Full Information Maximum Likelihood (FIML is presented. Finally a comparison between the FI LODE new and old version together with few words of conclusion conclude the paper.
Prediction of toxicity of nitrobenzenes using ab initio and least squares support vector machines
Energy Technology Data Exchange (ETDEWEB)
Niazi, Ali [Department of Chemistry, Faculty of Sciences, Azad University of Arak, Arak (Iran, Islamic Republic of)], E-mail: ali.niazi@gmail.com; Jameh-Bozorghi, Saeed; Nori-Shargh, Davood [Department of Chemistry, Faculty of Sciences, Azad University of Arak, Arak (Iran, Islamic Republic of)
2008-03-01
A quantitative structure-property relationship (QSPR) study is suggested for the prediction of toxicity (IGC{sub 50}) of nitrobenzenes. Ab initio theory was used to calculate some quantum chemical descriptors including electrostatic potentials and local charges at each atom, HOMO and LUMO energies, etc. Modeling of the IGC{sub 50} of nitrobenzenes as a function of molecular structures was established by means of the least squares support vector machines (LS-SVM). This model was applied for the prediction of the toxicity (IGC{sub 50}) of nitrobenzenes, which were not in the modeling procedure. The resulted model showed high prediction ability with root mean square error of prediction of 0.0049 for LS-SVM. Results have shown that the introduction of LS-SVM for quantum chemical descriptors drastically enhances the ability of prediction in QSAR studies superior to multiple linear regression and partial least squares.
Optimal Knot Selection for Least-squares Fitting of Noisy Data with Spline Functions
Energy Technology Data Exchange (ETDEWEB)
Jerome Blair
2008-05-15
An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.
Directory of Open Access Journals (Sweden)
Pan Jin-Shui
2009-05-01
Full Text Available Abstract Background Transfection in mammalian cells based on liposome presents great challenge for biological professionals. To protect themselves from exogenous insults, mammalian cells tend to manifest poor transfection efficiency. In order to gain high efficiency, we have to optimize several conditions of transfection, such as amount of liposome, amount of plasmid, and cell density at transfection. However, this process may be time-consuming and energy-consuming. Fortunately, several mathematical methods, developed in the past decades, may facilitate the resolution of this issue. This study investigates the possibility of optimizing transfection efficiency by using a method referred to as least-squares support vector machine, which requires only a few experiments and maintains fairly high accuracy. Results A protocol consists of 15 experiments was performed according to the principle of uniform design. In this protocol, amount of liposome, amount of plasmid, and the number of seeded cells 24 h before transfection were set as independent variables and transfection efficiency was set as dependent variable. A model was deduced from independent variables and their respective dependent variable. Another protocol made up by 10 experiments was performed to test the accuracy of the model. The model manifested a high accuracy. Compared to traditional method, the integrated application of uniform design and least-squares support vector machine greatly reduced the number of required experiments. What's more, higher transfection efficiency was achieved. Conclusion The integrated application of uniform design and least-squares support vector machine is a simple technique for obtaining high transfection efficiency. Using this novel method, the number of required experiments would be greatly cut down while higher efficiency would be gained. Least-squares support vector machine may be applicable to many other problems that need to be optimized.
Learning rates of least-square regularized regression with polynomial kernels
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in Lρ2X with Borel probability measure.
Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems
Van Benthem, Mark H.; Keenan, Michael R.
2008-11-11
A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.
Least-Squares Solutions of the Equation AX = B Over Anti-Hermitian Generalized Hamiltonian Matrices
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Upon using the denotative theorem of anti-Hermitian generalized Hamiltonian matrices, we solve effectively the least-squares problem min ‖AX - B‖ over anti-Hermitian generalized Hamiltonian matrices. We derive some necessary and sufficient conditions for solvability of the problem and an expression for general solution of the matrix equation AX = B. In addition, we also obtain the expression for the solution of a relevant optimal approximate problem.
Least squares algorithm for region-of-interest evaluation in emission tomography
Energy Technology Data Exchange (ETDEWEB)
Formiconi, A.R. (Sezione di Medicina Nucleare, Firenze (Italy). Dipt. di Fisiopatologia Clinica)
1993-03-01
In a simulation study, the performances of the least squares algorithm applied to region-of-interest evaluation were studied. The least squares algorithm is a direct algorithm which does not require any iterative computation scheme and also provides estimates of statistical uncertainties of the region-of-interest values (covariance matrix). A model of physical factors, such as system resolution, attenuation and scatter, can be specified in the algorithm. In this paper an accurate model of the non-stationary geometrical response of a camera-collimator system was considered. The algorithm was compared with three others which are specialized for region-of-interest evaluation, as well as with the conventional method of summing the reconstructed quantity over the regions of interest. For the latter method, two algorithms were used for image reconstruction; these included filtered back projection and conjugate gradient least squares with the model of nonstationary geometrical response. For noise-free data and for regions of accurate shape least squares estimates were unbiased within roundoff errors. For noisy data, estimates were still unbiased but precision worsened for regions smaller than resolution: simulating typical statistics of brain perfusion studies performed with a collimated camera, the estimated standard deviation for a 1 cm square region was 10% with an ultra high-resolution collimator and 7% with a low energy all purpose collimator. Conventional region-of-interest estimates showed comparable precision but were heavily biased if filtered back projection was employed for image reconstruction. Using the conjugate gradient iterative algorithm and the model of nonstationary geometrical response, bias of estimates decreased on increasing the number of iterations, but precision worsened thus achieving an estimated standard deviation of more than 25% for the same 1 cm region.
Directory of Open Access Journals (Sweden)
H. Hüseyin SAYAN
2009-01-01
Full Text Available In this study, recursive least squares method (RLSM that is one of the adaptable classical methods was used. Firstly forgetting factor was adapted to RLSM. Phase information of voltage signal belonging to an electric power network that contains harmonics and spike was obtained by developed approach. Then responses of the algorithm were investigated for voltage collapse, phase shift and spike. Simulation was implemented by using MATLAB® code. Results of simulation were examined and efficiency of method was presented.
Chen, S; Wu, Y; Luk, B L
1999-01-01
The paper presents a two-level learning method for radial basis function (RBF) networks. A regularized orthogonal least squares (ROLS) algorithm is employed at the lower level to construct RBF networks while the two key learning parameters, the regularization parameter and the RBF width, are optimized using a genetic algorithm (GA) at the upper level. Nonlinear time series modeling and prediction is used as an example to demonstrate the effectiveness of this hierarchical learning approach.
Sherstinsky, A; Picard, R W
1996-01-01
The efficiency of the orthogonal least squares (OLS) method for training approximation networks is examined using the criterion of energy compaction. We show that the selection of basis vectors produced by the procedure is not the most compact when the approximation is performed using a nonorthogonal basis. Hence, the algorithm does not produce the smallest possible networks for a given approximation error. Specific examples are given using the Gaussian radial basis functions type of approximation networks.
Least squares adjustment of large-scale geodetic networks by orthogonal decomposition
Energy Technology Data Exchange (ETDEWEB)
George, J.A.; Golub, G.H.; Heath, M.T.; Plemmons, R.J.
1981-11-01
This article reviews some recent developments in the solution of large sparse least squares problems typical of those arising in geodetic adjustment problems. The new methods are distinguished by their use of orthogonal transformations which tend to improve numerical accuracy over the conventional approach based on the use of the normal equations. The adaptation of these new schemes to allow for the use of auxiliary storage and their extension to rank deficient problems are also described.
Solving the Axisymmetric Inverse Heat Conduction Problem by a Wavelet Dual Least Squares Method
Directory of Open Access Journals (Sweden)
Fu Chu-Li
2009-01-01
Full Text Available We consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. This problem is ill-posed; the solution (if it exists does not depend continuously on the data. A special project method—dual least squares method generated by the family of Shannon wavelet is applied to formulate regularized solution. Meanwhile, an order optimal error estimate between the approximate solution and exact solution is proved.
Modelling of the Relaxation Least Squares-Based Neural Networks and Its Application
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A relaxation least squares-based learning algorithm for neural networks is proposed. Not only does it have a fast convergence rate, but it involves less computation quantity. Therefore, it is suitable to deal with the case when a network has a large scale but the number of training data is very limited. It has been used in converting furnace process modelling, and impressive result has been obtained.
A weighted least-squares method for parameter estimation in structured models
Galrinho, Miguel; Rojas, Cristian R.; Hjalmarsson, Håkan
2014-01-01
Parameter estimation in structured models is generally considered a difficult problem. For example, the prediction error method (PEM) typically gives a non-convex optimization problem, while it is difficult to incorporate structural information in subspace identification. In this contribution, we revisit the idea of iteratively using the weighted least-squares method to cope with the problem of non-convex optimization. The method is, essentially, a three-step method. First, a high order least...
Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine
Institute of Scientific and Technical Information of China (English)
XU Rui-Rui; BIAN Guo-Xing; GAO Chen-Feng; CHEN Tian-Lun
2005-01-01
The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction.First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.
A Backward Stable Hyperbolic QR Factorization Method for Solving Indefinite Least Squares Problem
Institute of Scientific and Technical Information of China (English)
徐洪国
2004-01-01
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix,Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several trian-gular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient thanthe backward stable method proposed by Chandrasekaran, Gu and Sayed.
A DYNAMICAL SYSTEM ALGORITHM FOR SOLVING A LEAST SQUARES PROBLEM WITH ORTHOGONALITY CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
黄建国; 叶中行; 徐雷
2001-01-01
This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero-extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.
Seismic time-lapse imaging using Interferometric least-squares migration
Sinha, Mrinal
2016-09-06
One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.
LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The main purpose of reverse engineering is to convert discrete data points into piecewise smooth, continuous surface models.Before carrying out model reconstruction it is significant to extract geometric features because the quality of modeling greatly depends on the representation of features.Some fitting techniques of natural quadric surfaces with least-squares method are described.And these techniques can be directly used to extract quadric surfaces features during the process of segmentation for point cloud.
Least-Squares Data Adjustment with Rank-Deficient Data Covariance Matrices
Energy Technology Data Exchange (ETDEWEB)
Williams, J.G. [The University of Arizona, Tucson, AZ 85721-0119 (United States)
2011-07-01
A derivation of the linear least-squares adjustment formulae is required that avoids the assumption that the covariance matrix of prior parameters can be inverted. Possible proofs are of several kinds, including: (i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. In this paper, the least-squares adjustment equations are derived in both these ways, while explicitly assuming that the covariance matrix of prior parameters is singular. It will be proved that the solutions are unique and that, contrary to statements that have appeared in the literature, the least-squares adjustment problem is not ill-posed. No modification is required to the adjustment formulae that have been used in the past in the case of a singular covariance matrix for the priors. In conclusion: The linear least-squares adjustment formula that has been used in the past is valid in the case of a singular covariance matrix for the covariance matrix of prior parameters. Furthermore, it provides a unique solution. Statements in the literature, to the effect that the problem is ill-posed are wrong. No regularization of the problem is required. This has been proved in the present paper by two methods, while explicitly assuming that the covariance matrix of prior parameters is singular: i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. No modification is needed to the adjustment formulae that have been used in the past. (author)
Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem
Directory of Open Access Journals (Sweden)
Baiyu Wang
2014-01-01
Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.
Wang, Youhua; Nakayama, Kenji
1995-01-01
In this letter, we introduce a predictor based least square (PLS) algorithm. By involving both order- and time-update recursions, the PLS algorithm is found to have a more stable performance compared with the stable version (Version II) of the RLS algorithm shown in Ref. [1]. Nevertheless, the computational requirement is about 50% of that of the RLS algorithm. As an application, the PLS algorithm can be applied to the fast newton transversal filters (FNTF) [2]. The FNTF algorithms suffer fro...
Constrained Balancing of Two Industrial Rotor Systems: Least Squares and Min-Max Approaches
Directory of Open Access Journals (Sweden)
Bin Huang
2009-01-01
Full Text Available Rotor vibrations caused by rotor mass unbalance distributions are a major source of maintenance problems in high-speed rotating machinery. Minimizing this vibration by balancing under practical constraints is quite important to industry. This paper considers balancing of two large industrial rotor systems by constrained least squares and min-max balancing methods. In current industrial practice, the weighted least squares method has been utilized to minimize rotor vibrations for many years. One of its disadvantages is that it cannot guarantee that the maximum value of vibration is below a specified value. To achieve better balancing performance, the min-max balancing method utilizing the Second Order Cone Programming (SOCP with the maximum correction weight constraint, the maximum residual response constraint as well as the weight splitting constraint has been utilized for effective balancing. The min-max balancing method can guarantee a maximum residual vibration value below an optimum value and is shown by simulation to significantly outperform the weighted least squares method.
A least square extrapolation method for improving solution accuracy of PDE computations
Garbey, M
2003-01-01
Richardson extrapolation (RE) is based on a very simple and elegant mathematical idea that has been successful in several areas of numerical analysis such as quadrature or time integration of ODEs. In theory, RE can be used also on PDE approximations when the convergence order of a discrete solution is clearly known. But in practice, the order of a numerical method often depends on space location and is not accurately satisfied on different levels of grids used in the extrapolation formula. We propose in this paper a more robust and numerically efficient method based on the idea of finding automatically the order of a method as the solution of a least square minimization problem on the residual. We introduce a two-level and three-level least square extrapolation method that works on nonmatching embedded grid solutions via spline interpolation. Our least square extrapolation method is a post-processing of data produced by existing PDE codes, that is easy to implement and can be a better tool than RE for code v...
Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions
Qiao, Bingqiang; Zeng, Houdun; Li, Xiang; Dai, Benzhong
2015-01-01
With the standard deviation for the logarithm of the re-scaled range $\\langle |F(t+\\tau)-F(t)|\\rangle$ of simulated fractal Brownian motions $F(t)$ given in a previous paper \\cite{q14}, the method of least squares is adopted to determine the slope, $S$, and intercept, $I$, of the log$(\\langle |F(t+\\tau)-F(t)|\\rangle)$ vs $\\rm{log}(\\tau)$ plot to investigate the limitation of this procedure. It is found that the reduced $\\chi^2$ of the fitting decreases with the increase of the Hurst index, $H$ (the expectation value of $S$), which may be attributed to the correlation among the re-scaled ranges. Similarly, it is found that the errors of the fitting parameters $S$ and $I$ are usually smaller than their corresponding standard deviations. These results show the limitation of using the simple least square method to determine the dimension of a fractal time series. Nevertheless, they may be used to reinterpret the fitting results of the least square method to determine the dimension of fractal Brownian motions more...
A least-squares computational ``tool kit``. Nuclear data and measurements series
Energy Technology Data Exchange (ETDEWEB)
Smith, D.L.
1993-04-01
The information assembled in this report is intended to offer a useful computational ``tool kit`` to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications.
Cao, Jiguo
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Luo, Wei-Ping; Li, Hong-Qi; Shi, Ning
2016-06-01
At the early stages of deep-water oil exploration and development, fewer and further apart wells are drilled than in onshore oilfields. Supervised least squares support vector machine algorithms are used to predict the reservoir parameters but the prediction accuracy is low. We combined the least squares support vector machine (LSSVM) algorithm with semi-supervised learning and established a semi-supervised regression model, which we call the semi-supervised least squares support vector machine (SLSSVM) model. The iterative matrix inversion is also introduced to improve the training ability and training time of the model. We use the UCI data to test the generalization of a semi-supervised and a supervised LSSVM models. The test results suggest that the generalization performance of the LSSVM model greatly improves and with decreasing training samples the generalization performance is better. Moreover, for small-sample models, the SLSSVM method has higher precision than the semi-supervised K-nearest neighbor (SKNN) method. The new semisupervised LSSVM algorithm was used to predict the distribution of porosity and sandstone in the Jingzhou study area.
A cross-correlation objective function for least-squares migration and visco-acoustic imaging
Dutta, Gaurav
2014-08-05
Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.
Cao, Jiguo; Huang, Jianhua Z; Wu, Hulin
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Cross-correlation least-squares reverse time migration in the pseudo-time domain
Li, Qingyang; Huang, Jianping; Li, Zhenchun
2017-08-01
The least-squares reverse time migration (LSRTM) method with higher image resolution and amplitude is becoming increasingly popular. However, the LSRTM is not widely used in field land data processing because of its sensitivity to the initial migration velocity model, large computational cost and mismatch of amplitudes between the synthetic and observed data. To overcome the shortcomings of the conventional LSRTM, we propose a cross-correlation least-squares reverse time migration algorithm in pseudo-time domain (PTCLSRTM). Our algorithm not only reduces the depth/velocity ambiguities, but also reduces the effect of velocity error on the imaging results. It relieves the accuracy requirements on the migration velocity model of least-squares migration (LSM). The pseudo-time domain algorithm eliminates the irregular wavelength sampling in the vertical direction, thus it can reduce the vertical grid points and memory requirements used during computation, which makes our method more computationally efficient than the standard implementation. Besides, for field data applications, matching the recorded amplitudes is a very difficult task because of the viscoelastic nature of the Earth and inaccuracies in the estimation of the source wavelet. To relax the requirement for strong amplitude matching of LSM, we extend the normalized cross-correlation objective function to the pseudo-time domain. Our method is only sensitive to the similarity between the predicted and the observed data. Numerical tests on synthetic and land field data confirm the effectiveness of our method and its adaptability for complex models.
Sun, Zhibin; Chang, Chein-I.; Ren, Hsuan; D"Amico, Francis M.; Jensen, James O.
2003-12-01
Fully constrained linear spectral mixture analysis (FCLSMA) has been used for material quantification in remotely sensed imagery. In order to implement FCLSMA, two constraints are imposed on abundance fractions, referred to as Abundance Sum-to-one Constraint (ASC) and Abundance Nonnegativity Constraint (ANC). While the ASC is linear equality constraint, the ANC is a linear inequality constraint. A direct approach to imposing the ASC and ANC has been recently investigated and is called fully constrained least-squares (FCLS) method. Since there is no analytical solution resulting from the ANC, a modified fully constrained least-squares method (MFCLS) which replaces the ANC with an Absolute Abundance Sum-to-one Constraint (AASC) was proposed to convert a set of inequality constraints to a quality constraint. The results produced by these two approaches have been shown to be very close. In this paper, we take an oopposite approach to the MFCLS method, called least-squares with linear inequality constraints (LSLIC) method which also solves FCLSMA, but replaces the ASC with two linear inequalities. The proposed LSLIC transforms the FCLSMA to a linear distance programming problem which can be solved easily by a numerical algorithm. In order to demonstrate its utility in solving FCLSMA, the LSLIC method is compared to the FCLS and MFCLS methods. The experimental results show that these three methods perform very similarly with only subtle differences resulting from their problem formations.
Precision PEP-II optics measurement with an SVD-enhanced Least-Square fitting
Yan, Y. T.; Cai, Y.
2006-03-01
A singular value decomposition (SVD)-enhanced Least-Square fitting technique is discussed. By automatic identifying, ordering, and selecting dominant SVD modes of the derivative matrix that responds to the variations of the variables, the converging process of the Least-Square fitting is significantly enhanced. Thus the fitting speed can be fast enough for a fairly large system. This technique has been successfully applied to precision PEP-II optics measurement in which we determine all quadrupole strengths (both normal and skew components) and sextupole feed-downs as well as all BPM gains and BPM cross-plane couplings through Least-Square fitting of the phase advances and the Local Green's functions as well as the coupling ellipses among BPMs. The local Green's functions are specified by 4 local transfer matrix components R12, R34, R32, R14. These measurable quantities (the Green's functions, the phase advances and the coupling ellipse tilt angles and axis ratios) are obtained by analyzing turn-by-turn Beam Position Monitor (BPM) data with a high-resolution model-independent analysis (MIA). Once all of the quadrupoles and sextupole feed-downs are determined, we obtain a computer virtual accelerator which matches the real accelerator in linear optics. Thus, beta functions, linear coupling parameters, and interaction point (IP) optics characteristics can be measured and displayed.
Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution
Sen, Symal K.; Shaykhian, Gholam Ali
2011-01-01
Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.
Generalized total least squares prediction algorithm for universal 3D similarity transformation
Wang, Bin; Li, Jiancheng; Liu, Chao; Yu, Jie
2017-02-01
Three-dimensional (3D) similarity datum transformation is extensively applied to transform coordinates from GNSS-based datum to a local coordinate system. Recently, some total least squares (TLS) algorithms have been successfully developed to solve the universal 3D similarity transformation problem (probably with big rotation angles and an arbitrary scale ratio). However, their procedures of the parameter estimation and new point (non-common point) transformation were implemented separately, and the statistical correlation which often exists between the common and new points in the original coordinate system was not considered. In this contribution, a generalized total least squares prediction (GTLSP) algorithm, which implements the parameter estimation and new point transformation synthetically, is proposed. All of the random errors in the original and target coordinates, and their variance-covariance information will be considered. The 3D transformation model in this case is abstracted as a kind of generalized errors-in-variables (EIV) model and the equation for new point transformation is incorporated into the functional model as well. Then the iterative solution is derived based on the Gauss-Newton approach of nonlinear least squares. The performance of GTLSP algorithm is verified in terms of a simulated experiment, and the results show that GTLSP algorithm can improve the statistical accuracy of the transformed coordinates compared with the existing TLS algorithms for 3D similarity transformation.
Identifying differentially methylated genes using mixed effect and generalized least square models
2009-01-01
Abstract Background DNA methylation plays an important role in the process of tumorigenesis. Identifying differentially methylated genes or CpG islands (CGIs) associated with genes between two tumor subtypes is thus an important biological question. The methylation status of all CGIs in the whole genome can be assayed with differential methylation hybridization (DMH) microarrays. However, patient samples or cell lines are heterogeneous, so their methylation pattern may be very different. In a...
Zhang, Hong-Guang; Yang, Qin-Min; Lu, Jian-Gang
2014-04-01
In this paper, a novel discriminant methodology based on near infrared spectroscopic analysis technique and least square support vector machine was proposed for rapid and nondestructive discrimination of different types of Polyacrylamide. The diffuse reflectance spectra of samples of Non-ionic Polyacrylamide, Anionic Polyacrylamide and Cationic Polyacrylamide were measured. Then principal component analysis method was applied to reduce the dimension of the spectral data and extract of the principal compnents. The first three principal components were used for cluster analysis of the three different types of Polyacrylamide. Then those principal components were also used as inputs of least square support vector machine model. The optimization of the parameters and the number of principal components used as inputs of least square support vector machine model was performed through cross validation based on grid search. 60 samples of each type of Polyacrylamide were collected. Thus a total of 180 samples were obtained. 135 samples, 45 samples for each type of Polyacrylamide, were randomly split into a training set to build calibration model and the rest 45 samples were used as test set to evaluate the performance of the developed model. In addition, 5 Cationic Polyacrylamide samples and 5 Anionic Polyacrylamide samples adulterated with different proportion of Non-ionic Polyacrylamide were also prepared to show the feasibilty of the proposed method to discriminate the adulterated Polyacrylamide samples. The prediction error threshold for each type of Polyacrylamide was determined by F statistical significance test method based on the prediction error of the training set of corresponding type of Polyacrylamide in cross validation. The discrimination accuracy of the built model was 100% for prediction of the test set. The prediction of the model for the 10 mixing samples was also presented, and all mixing samples were accurately discriminated as adulterated samples. The
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Clustering technique-based least square support vector machine for EEG signal classification.
Siuly; Li, Yan; Wen, Peng Paul
2011-12-01
This paper presents a new approach called clustering technique-based least square support vector machine (CT-LS-SVM) for the classification of EEG signals. Decision making is performed in two stages. In the first stage, clustering technique (CT) has been used to extract representative features of EEG data. In the second stage, least square support vector machine (LS-SVM) is applied to the extracted features to classify two-class EEG signals. To demonstrate the effectiveness of the proposed method, several experiments have been conducted on three publicly available benchmark databases, one for epileptic EEG data, one for mental imagery tasks EEG data and another one for motor imagery EEG data. Our proposed approach achieves an average sensitivity, specificity and classification accuracy of 94.92%, 93.44% and 94.18%, respectively, for the epileptic EEG data; 83.98%, 84.37% and 84.17% respectively, for the motor imagery EEG data; and 64.61%, 58.77% and 61.69%, respectively, for the mental imagery tasks EEG data. The performance of the CT-LS-SVM algorithm is compared in terms of classification accuracy and execution (running) time with our previous study where simple random sampling with a least square support vector machine (SRS-LS-SVM) was employed for EEG signal classification. We also compare the proposed method with other existing methods in the literature for the three databases. The experimental results show that the proposed algorithm can produce a better classification rate than the previous reported methods and takes much less execution time compared to the SRS-LS-SVM technique. The research findings in this paper indicate that the proposed approach is very efficient for classification of two-class EEG signals.
Nakano, Takemi; Nagata, Kentaro; Yamada, Masafumi; Magatani, Kazushige
2009-01-01
In this study, we describe the application of least square method for muscular strength estimation in hand motion recognition based on surface electromyogram (SEMG). Although the muscular strength can consider the various evaluation methods, a grasp force is applied as an index to evaluate the muscular strength. Today, SEMG, which is measured from skin surface, is widely used as a control signal for many devices. Because, SEMG is one of the most important biological signal in which the human motion intention is directly reflected. And various devices using SEMG are reported by lots of researchers. Those devices which use SEMG as a control signal, we call them SEMG system. In SEMG system, to achieve high accuracy recognition is an important requirement. Conventionally SEMG system mainly focused on how to achieve this objective. Although it is also important to estimate muscular strength of motions, most of them cannot detect power of muscle. The ability to estimate muscular strength is a very important factor to control the SEMG systems. Thus, our objective of this study is to develop the estimation method for muscular strength by application of least square method, and reflecting the result of measured power to the controlled object. Since it was known that SEMG is formed by physiological variations in the state of muscle fiber membranes, it is thought that it can be related with grasp force. We applied to the least-squares method to construct a relationship between SEMG and grasp force. In order to construct an effective evaluation model, four SEMG measurement locations in consideration of individual difference were decided by the Monte Carlo method.
A hybrid least squares and principal component analysis algorithm for Raman spectroscopy.
Directory of Open Access Journals (Sweden)
Dominique Van de Sompel
Full Text Available Raman spectroscopy is a powerful technique for detecting and quantifying analytes in chemical mixtures. A critical part of Raman spectroscopy is the use of a computer algorithm to analyze the measured Raman spectra. The most commonly used algorithm is the classical least squares method, which is popular due to its speed and ease of implementation. However, it is sensitive to inaccuracies or variations in the reference spectra of the analytes (compounds of interest and the background. Many algorithms, primarily multivariate calibration methods, have been proposed that increase robustness to such variations. In this study, we propose a novel method that improves robustness even further by explicitly modeling variations in both the background and analyte signals. More specifically, it extends the classical least squares model by allowing the declared reference spectra to vary in accordance with the principal components obtained from training sets of spectra measured in prior characterization experiments. The amount of variation allowed is constrained by the eigenvalues of this principal component analysis. We compare the novel algorithm to the least squares method with a low-order polynomial residual model, as well as a state-of-the-art hybrid linear analysis method. The latter is a multivariate calibration method designed specifically to improve robustness to background variability in cases where training spectra of the background, as well as the mean spectrum of the analyte, are available. We demonstrate the novel algorithm's superior performance by comparing quantitative error metrics generated by each method. The experiments consider both simulated data and experimental data acquired from in vitro solutions of Raman-enhanced gold-silica nanoparticles.
A hybrid least squares and principal component analysis algorithm for Raman spectroscopy.
Van de Sompel, Dominique; Garai, Ellis; Zavaleta, Cristina; Gambhir, Sanjiv Sam
2012-01-01
Raman spectroscopy is a powerful technique for detecting and quantifying analytes in chemical mixtures. A critical part of Raman spectroscopy is the use of a computer algorithm to analyze the measured Raman spectra. The most commonly used algorithm is the classical least squares method, which is popular due to its speed and ease of implementation. However, it is sensitive to inaccuracies or variations in the reference spectra of the analytes (compounds of interest) and the background. Many algorithms, primarily multivariate calibration methods, have been proposed that increase robustness to such variations. In this study, we propose a novel method that improves robustness even further by explicitly modeling variations in both the background and analyte signals. More specifically, it extends the classical least squares model by allowing the declared reference spectra to vary in accordance with the principal components obtained from training sets of spectra measured in prior characterization experiments. The amount of variation allowed is constrained by the eigenvalues of this principal component analysis. We compare the novel algorithm to the least squares method with a low-order polynomial residual model, as well as a state-of-the-art hybrid linear analysis method. The latter is a multivariate calibration method designed specifically to improve robustness to background variability in cases where training spectra of the background, as well as the mean spectrum of the analyte, are available. We demonstrate the novel algorithm's superior performance by comparing quantitative error metrics generated by each method. The experiments consider both simulated data and experimental data acquired from in vitro solutions of Raman-enhanced gold-silica nanoparticles.
Local classification: Locally weighted-partial least squares-discriminant analysis (LW-PLS-DA).
Bevilacqua, Marta; Marini, Federico
2014-08-01
The possibility of devising a simple, flexible and accurate non-linear classification method, by extending the locally weighted partial least squares (LW-PLS) approach to the cases where the algorithm is used in a discriminant way (partial least squares discriminant analysis, PLS-DA), is presented. In particular, to assess which category an unknown sample belongs to, the proposed algorithm operates by identifying which training objects are most similar to the one to be predicted and building a PLS-DA model using these calibration samples only. Moreover, the influence of the selected training samples on the local model can be further modulated by adopting a not uniform distance-based weighting scheme which allows the farthest calibration objects to have less impact than the closest ones. The performances of the proposed locally weighted-partial least squares-discriminant analysis (LW-PLS-DA) algorithm have been tested on three simulated data sets characterized by a varying degree of non-linearity: in all cases, a classification accuracy higher than 99% on external validation samples was achieved. Moreover, when also applied to a real data set (classification of rice varieties), characterized by a high extent of non-linearity, the proposed method provided an average correct classification rate of about 93% on the test set. By the preliminary results, showed in this paper, the performances of the proposed LW-PLS-DA approach have proved to be comparable and in some cases better than those obtained by other non-linear methods (k nearest neighbors, kernel-PLS-DA and, in the case of rice, counterpropagation neural networks).
Analysis Linking the Tensor Structure to the Least-Squares Method.
1984-01-01
7 A-A142 159 ANALYSIS LINKIN THE TENSOR STRUCTURE TO THE LEAST-SQUARES METHOD(U) NOVA UNIV OCEANOGRAPHIC CENTER DANIA FL G BLAHA JAN 84 AFGL-TR-84...Tienstra ([5], [6], [7]), Baarda (C81, [9], [10]), Kooimans ([11]) and a number of others (for example, the editors of [71). It would probably be more...institute, Technische Hogeschool, Delft, 1967 & 1970. 11. A. H. KOOIMANS : "Principles of the Calculus of Observations". Rapport Special, Neuvi me Congr
Application of the Marquardt least-squares method to the estimation of pulse function parameters
Lundengârd, Karl; Rančić, Milica; Javor, Vesna; Silvestrov, Sergei
2014-12-01
Application of the Marquardt least-squares method (MLSM) to the estimation of non-linear parameters of functions used for representing various lightning current waveshapes is presented in this paper. Parameters are determined for the Pulse, Heidler's and DEXP function representing the first positive, first and subsequent negative stroke currents as given in IEC 62305-1 Standard Ed.2, and also for some other fast- and slow-decaying lightning current waveshapes. The results prove the ability of the MLSM to be used for the estimation of parameters of the functions important in lightning discharge modeling.
Huang, Lei; Asundi, Anand Krishna
2013-08-20
A framework with a combination of the radial basis functions (RBFs) method and the least-squares integration method is proposed to improve the integration process from gradient to shape. The principle of the framework is described, and the performance of the proposed method is investigated by simulation. Improvement in accuracy is verified by comparing the result with the usual RBFs-based subset-by-subset stitching method. The proposed method is accurate, automatic, easily implemented, and robust and even works with incomplete data.
Ribeiro, F B; Carlos, D U; Hiodo, F Y; Strobino, E F
2005-01-01
In this study, a least squares procedure for calculating the calibration constants of a portable gamma-ray spectrometer using the general inverse matrix method is presented. The procedure weights the model equations fitting to the calibration data, taking into account the variances in the counting rates and in the radioactive standard concentrations. The application of the described procedure is illustrated by calibrating twice the same gamma-ray spectrometer, with two independent data sets collected approximately 18 months apart in the same calibration facility.
Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique
Institute of Scientific and Technical Information of China (English)
Jiang-Tao Su; Hong-Qi Zhang
2004-01-01
To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station(HSOS),we scanned the FeIλ5324.19 A line over the wavelength interval from 150mA redward of the line center to 150mA blueward,in steps of 10mA.With the technique of analytic inversion of Stokes profiles via nonlinear least-squares,we present the calibration coefficients for the HSOS vector magnetic magnetogram.We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.
Thrust estimator design based on least squares support vector regression machine
Institute of Scientific and Technical Information of China (English)
ZHAO Yong-ping; SUN Jian-guo
2010-01-01
In order to realize direct thrust control instead of traditional sensor-based control for nero-engines,it is indispensable to design a thrust estimator with high accuracy,so a scheme for thrust estimator design based on the least square support vector regression machine is proposed to solve this problem.Furthermore,numerical simulations confirm the effectiveness of our presented scheme.During the process of estimator design,a wrap per criterion that can not only reduce the computational complexity but also enhance the generalization performance is proposed to select variables as input variables for estimator.
Solving sparse linear least squares problems on some supercomputers by using large dense blocks
DEFF Research Database (Denmark)
Hansen, Per Christian; Ostromsky, T; Sameh, A;
1997-01-01
technique is preferable to sparse matrix technique when the matrices are not large, because the high computational speed compensates fully the disadvantages of using more arithmetic operations and more storage. For very large matrices the computations must be organized as a sequence of tasks in each...... the matrix so that dense blocks can be constructed and treated with some standard software, say LAPACK or NAG. These ideas are implemented for linear least-squares problems. The rectangular matrices (that appear in such problems) are decomposed by an orthogonal method. Results obtained on a CRAY C92A...
SPARSE REPRESENTATIONS WITH DATA FIDELITY TERM VIA AN ITERATIVELY REWEIGHTED LEAST SQUARES ALGORITHM
Energy Technology Data Exchange (ETDEWEB)
WOHLBERG, BRENDT [Los Alamos National Laboratory; RODRIGUEZ, PAUL [Los Alamos National Laboratory
2007-01-08
Basis Pursuit and Basis Pursuit Denoising, well established techniques for computing sparse representations, minimize an {ell}{sup 2} data fidelity term subject to an {ell}{sup 1} sparsity constraint or regularization term on the solution by mapping the problem to a linear or quadratic program. Basis Pursuit Denoising with an {ell}{sup 1} data fidelity term has recently been proposed, also implemented via a mapping to a linear program. They introduce an alternative approach via an iteratively Reweighted Least Squares algorithm, providing greater flexibility in the choice of data fidelity term norm, and computational advantages in certain circumstances.
A least squares approach for efficient and reliable short-term versus long-term optimization
DEFF Research Database (Denmark)
Christiansen, Lasse Hjuler; Capolei, Andrea; Jørgensen, John Bagterp
2017-01-01
the balance between the objectives, leaving an unfulfilled potential to increase profits. To promote efficient and reliable short-term versus long-term optimization, this paper introduces a natural way to characterize desirable Pareto points and proposes a novel least squares (LS) method. Unlike hierarchical...... approaches, the method is guaranteed to converge to a Pareto optimal point. Also, the LS method is designed to properly balance multiple objectives, independently of Pareto front’s shape. As such, the method poses a practical alternative to a posteriori methods in situations where the frontier is intractable...
On-line Weighted Least Squares Kernel Method for Nonlinear Dynamic Modeling
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Support vector machines (SVM) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on rolling optimization method and on-line learning strategies, a novel approach based on weighted least squares support vector machines (WLS-SVM) is proposed for nonlinear dynamic modeling.The good robust property of the novel approach enhances the generalization ability of kernel method-based modeling and some experimental results are presented to illustrate the feasibility of the proposed method.
Speed control of induction motor using fuzzy recursive least squares technique
Directory of Open Access Journals (Sweden)
Santiago Sánchez
2008-12-01
Full Text Available A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the control system.
Energy Technology Data Exchange (ETDEWEB)
Griffin, P.J.
1998-05-01
This report provides a review of the Palisades submittal to the Nuclear Regulatory Commission requesting endorsement of their accumulated neutron fluence estimates based on a least squares adjustment methodology. This review highlights some minor issues in the applied methodology and provides some recommendations for future work. The overall conclusion is that the Palisades fluence estimation methodology provides a reasonable approach to a {open_quotes}best estimate{close_quotes} of the accumulated pressure vessel neutron fluence and is consistent with the state-of-the-art analysis as detailed in community consensus ASTM standards.
Extracting information from two-dimensional electrophoresis gels by partial least squares regression
DEFF Research Database (Denmark)
Jessen, Flemming; Lametsch, R.; Bendixen, E.;
2002-01-01
of all proteins/spots in the gels. In the present study it is demonstrated how information can be extracted by multivariate data analysis. The strategy is based on partial least squares regression followed by variable selection to find proteins that individually or in combination with other proteins vary......Two-dimensional gel electrophoresis (2-DE) produces large amounts of data and extraction of relevant information from these data demands a cautious and time consuming process of spot pattern matching between gels. The classical approach of data analysis is to detect protein markers that appear...
Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis.
Wang, Xin; Li, Yan; Wei, Haoyun; Chen, Xia
2016-10-26
Classical least squares (CLS) regression is a popular multivariate statistical method used frequently for quantitative analysis using Fourier transform infrared (FT-IR) spectrometry. Classical least squares provides the best unbiased estimator for uncorrelated residual errors with zero mean and equal variance. However, the noise in FT-IR spectra, which accounts for a large portion of the residual errors, is heteroscedastic. Thus, if this noise with zero mean dominates in the residual errors, the weighted least squares (WLS) regression method described in this paper is a better estimator than CLS. However, if bias errors, such as the residual baseline error, are significant, WLS may perform worse than CLS. In this paper, we compare the effect of noise and bias error in using CLS and WLS in quantitative analysis. Results indicated that for wavenumbers with low absorbance, the bias error significantly affected the error, such that the performance of CLS is better than that of WLS. However, for wavenumbers with high absorbance, the noise significantly affected the error, and WLS proves to be better than CLS. Thus, we propose a selective weighted least squares (SWLS) regression that processes data with different wavenumbers using either CLS or WLS based on a selection criterion, i.e., lower or higher than an absorbance threshold. The effects of various factors on the optimal threshold value (OTV) for SWLS have been studied through numerical simulations. These studies reported that: (1) the concentration and the analyte type had minimal effect on OTV; and (2) the major factor that influences OTV is the ratio between the bias error and the standard deviation of the noise. The last part of this paper is dedicated to quantitative analysis of methane gas spectra, and methane/toluene mixtures gas spectra as measured using FT-IR spectrometry and CLS, WLS, and SWLS. The standard error of prediction (SEP), bias of prediction (bias), and the residual sum of squares of the errors
Recursive Least Squares Estimator with Multiple Exponential Windows in Vector Autoregression
Institute of Scientific and Technical Information of China (English)
Hong-zhi An; Zhi-guo Li
2002-01-01
In the parameter tracking of time-varying systems, the ordinary method is weighted least squares with the rectangular window or the exponential window. In this paper we propose a new kind of sliding window called the multiple exponential window, and then use it to fit time-varying Gaussian vector autoregressive models. The asymptotic bias and covariance of the estimator of the parameter for time-invariant models are also derived. Simulation results show that the multiple exponential windows have better parameter tracking effect than rectangular windows and exponential ones.
An Improved Algorithm of Grounding Grids Corrosion Diagnosis Based on Total Least Square Method
Institute of Scientific and Technical Information of China (English)
ZHANG Ying-jiao; NIU Tao; WANG Sen
2011-01-01
A new model considering corrosion property for grounding grids diagnosis is proposed, which provides reference solutions of ambiguous branches. The constraint total least square method based on singular value decomposition is adopted to improve the effectiveness of grounding grids' diagnosis algorithm. The improvement can weaken the influence of the model's error, which results from the differences between design paper and actual grid. Its influence on touch and step voltages caused by the interior resistance of conductors is taken into account. Simulation results show the validity of this approach.
Normalized least-squares estimation in time-varying ARCH models
Fryzlewicz, Piotr; Sapatinas, Theofanis; Subba Rao, Suhasini
2008-01-01
We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. ¶ Since the parameters are changing over time, a successful estimator needs to perform well for small samples. We propose a kernel normalized-least-squares (kernel-NLS) estimator which has a closed form...
A Weighted Least-Squares Approach to Parameter Estimation Problems Based on Binary Measurements
Colinet, Eric; Juillard, Jérôme
2010-01-01
We present a new approach to parameter estimation problems based on binary measurements, motivated by the need to add integrated low-cost self-test features to microfabricated devices. This approach is based on the use of original weighted least-squares criteria: as opposed to other existing methods, it requires no dithering signal and it does not rely on an approximation of the quantizer. In this paper, we focus on a simple choice for the weights and establish some asymptotical properties of...
Circular and linear regression fitting circles and lines by least squares
Chernov, Nikolai
2010-01-01
Find the right algorithm for your image processing applicationExploring the recent achievements that have occurred since the mid-1990s, Circular and Linear Regression: Fitting Circles and Lines by Least Squares explains how to use modern algorithms to fit geometric contours (circles and circular arcs) to observed data in image processing and computer vision. The author covers all facets-geometric, statistical, and computational-of the methods. He looks at how the numerical algorithms relate to one another through underlying ideas, compares the strengths and weaknesses of each algorithm, and il
Useful and little-known applications of the Least Square Method and some consequences of covariances
Helene, Otaviano; Mariano, Leandro; Guimarães-Filho, Zwinglio
2016-10-01
Covariances are as important as variances when dealing with experimental data and they must be considered in fitting procedures and adjustments in order to preserve the statistical properties of the adjusted quantities. In this paper, we apply the Least Square Method in matrix form to several simple problems in order to evaluate the consequences of covariances in the fitting procedure. Among the examples, we demonstrate how a measurement of a physical quantity can change the adopted value of all other covariant quantities and how a new single point (x , y) improves the parameters of a previously adjusted straight-line.
Machado, A. E. de A.; da Gama, A. A. de S.; de Barros Neto, B.
2011-09-01
A partial least squares regression analysis of a large set of donor-acceptor organic molecules was performed to predict the magnitude of their static first hyperpolarizabilities ( β's). Polyenes, phenylpolyenes and biphenylpolyenes with augmented chain lengths displayed large β values, in agreement with the available experimental data. The regressors used were the HOMO-LUMO energy gap, the ground-state dipole moment, the HOMO energy AM1 values and the number of π-electrons. The regression equation predicts quite well the static β values for the molecules investigated and can be used to model new organic-based materials with enhanced nonlinear responses.
Least Squares Spectral Analysis and Its Application to Superconducting Gravimeter Data Analysis
Institute of Scientific and Technical Information of China (English)
YIN Hui; Spiros D. Pagiatakis
2004-01-01
Detection of a periodic signal hidden in noise is the goal of Superconducting Gravimeter (SG) data analysis. Due to spikes, gaps, datum shrifts (offsets) and other disturbances, the traditional FFT method shows inherent limitations. Instead, the least squares spectral analysis (LSSA) has showed itself more suitable than Fourier analysis of gappy, unequally spaced and unequally weighted data series in a variety of applications in geodesy and geophysics. This paper reviews the principle of LSSA and gives a possible strategy for the analysis of time series obtained from the Canadian Superconducting Gravimeter Installation (CGSI), with gaps, offsets, unequal sampling decimation of the data and unequally weighted data points.
Solving Time of Least Square Systems in Sigma-Pi Unit Networks
Courrieu, Pierre
2008-01-01
The solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve a system in a plausible neural architecture is critical. This paper presents a recurrent network of Sigma-Pi neurons, whose solving time increases at most like the logarithm of the system size, and of its condition number, which provides plausible computation times for biological systems.
Regularization Paths for Least Squares Problems with Generalized $\\ell_1$ Penalties
Tibshirani, Ryan J
2010-01-01
We present a path algorithm for least squares problems with generalized $\\ell_1$ penalties. This includes as a special case the lasso and fused lasso problems. The algorithm is based on solving the (equivalent) Lagrange dual problem, an approach which offers both a computational advantage and an interesting geometric interpretation of the solution path. Using insights gathered from the dual formulation, we study degrees of freedom for the generalized problem, and develop an unbiased estimate of the degrees of freedom of the fused lasso fit. Our approach bears similarities to least angle regression (LARS), and a simple modification to our method gives the LARS procedure exactly.
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Energy Technology Data Exchange (ETDEWEB)
Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)
1996-12-31
Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.
Optimization of absorption placement using geometrical acoustic models and least squares.
Saksela, Kai; Botts, Jonathan; Savioja, Lauri
2015-04-01
Given a geometrical model of a space, the problem of optimally placing absorption in a space to match a desired impulse response is in general nonlinear. This has led some to use costly optimization procedures. This letter reformulates absorption assignment as a constrained linear least-squares problem. Regularized solutions result in direct distribution of absorption in the room and can accommodate multiple frequency bands, multiple sources and receivers, and constraints on geometrical placement of absorption. The method is demonstrated using a beam tracing model, resulting in the optimal absorption placement on the walls and ceiling of a classroom.
Directory of Open Access Journals (Sweden)
Yan Zhou
2013-01-01
Full Text Available We propose an augmented classical least squares (ACLS calibration method for quantitative Raman spectral analysis against component information loss. The Raman spectral signals with low analyte concentration correlations were selected and used as the substitutes for unknown quantitative component information during the CLS calibration procedure. The number of selected signals was determined by using the leave-one-out root-mean-square error of cross-validation (RMSECV curve. An ACLS model was built based on the augmented concentration matrix and the reference spectral signal matrix. The proposed method was compared with partial least squares (PLS and principal component regression (PCR using one example: a data set recorded from an experiment of analyte concentration determination using Raman spectroscopy. A 2-fold cross-validation with Venetian blinds strategy was exploited to evaluate the predictive power of the proposed method. The one-way variance analysis (ANOVA was used to access the predictive power difference between the proposed method and existing methods. Results indicated that the proposed method is effective at increasing the robust predictive power of traditional CLS model against component information loss and its predictive power is comparable to that of PLS or PCR.
Directory of Open Access Journals (Sweden)
I Gusti Ayu Made Srinadi
2017-06-01
Full Text Available Partial Least Square Regression (PLSR is one of the methods applied in the estimation of multiple linear regression models when the ordinary least square method (OLS can not be used. OLS generates an invalid model estimate when multicollinearity occurs or when the number of independent variables is greater than the number of data observations. In conditions that OLS can be applied in obtaining model estimation, want to know the performance of PLSR method. This study aims to determine the model of PLSR the influence of literacy rate, the average of school duration, school enrollment rate, Income per capita, and open unemployment rate to the level of poverty seen from the percentage of poor people in Indonesia by 2015. Estimated model with OLS , Only variable of literacy rate are included in the model with the coefficient of determination R2 = 32.52%. PLSR model estimation of cross-validation, leave-one-out method with one selected component has R2 of 33,23%. Both models shows a negative relationship between poverty and literacy rate. The higher literacy rate will reduce the poverty level, indicating that the success of the Indonesian government in the development of education will support the government's success in reducing poverty level.
Confidence Region of Least Squares Solution for Single-Arc Observations
Principe, G.; Armellin, R.; Lewis, H.
2016-09-01
The total number of active satellites, rocket bodies, and debris larger than 10 cm is currently about 20,000. Considering all resident space objects larger than 1 cm this rises to an estimated minimum of 500,000 objects. Latest generation sensor networks will be able to detect small-size objects, producing millions of observations per day. Due to observability constraints it is likely that long gaps between observations will occur for small objects. This requires to determine the space object (SO) orbit and to accurately describe the associated uncertainty when observations are acquired on a single arc. The aim of this work is to revisit the classical least squares method taking advantage of the high order Taylor expansions enabled by differential algebra. In particular, the high order expansion of the residuals with respect to the state is used to implement an arbitrary order least squares solver, avoiding the typical approximations of differential correction methods. In addition, the same expansions are used to accurately characterize the confidence region of the solution, going beyond the classical Gaussian distributions. The properties and performances of the proposed method are discussed using optical observations of objects in LEO, HEO, and GEO.
Li, Chuang; Huang, Jian-Ping; Li, Zhen-Chun; Wang, Rong-Rong
2017-03-01
Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration (PLSRTM) method with singular spectrum constraint. Singular spectrum analysis (SSA) is used in the preconditioning of the take-offangle-domain common-image gathers (TADCIGs). In addition, we adopt randomized singular value decomposition (RSVD) to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition (SVD) of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.
Fitting of dihedral terms in classical force fields as an analytic linear least-squares problem.
Hopkins, Chad W; Roitberg, Adrian E
2014-07-28
The derivation and optimization of most energy terms in modern force fields are aided by automated computational tools. It is therefore important to have algorithms to rapidly and precisely train large numbers of interconnected parameters to allow investigators to make better decisions about the content of molecular models. In particular, the traditional approach to deriving dihedral parameters has been a least-squares fit to target conformational energies through variational optimization strategies. We present a computational approach for simultaneously fitting force field dihedral amplitudes and phase constants which is analytic within the scope of the data set. This approach completes the optimal molecular mechanics representation of a quantum mechanical potential energy surface in a single linear least-squares fit by recasting the dihedral potential into a linear function in the parameters. We compare the resulting method to a genetic algorithm in terms of computational time and quality of fit for two simple molecules. As suggested in previous studies, arbitrary dihedral phases are only necessary when modeling chiral molecules, which include more than half of drugs currently in use, so we also examined a dihedral parametrization case for the drug amoxicillin and one of its stereoisomers where the target dihedral includes a chiral center. Asymmetric dihedral phases are needed in these types of cases to properly represent the quantum mechanical energy surface and to differentiate between stereoisomers about the chiral center.
Zimmer, Christoph; Sahle, Sven
2016-04-01
Parameter estimation for models with intrinsic stochasticity poses specific challenges that do not exist for deterministic models. Therefore, specialized numerical methods for parameter estimation in stochastic models have been developed. Here, we study whether dedicated algorithms for stochastic models are indeed superior to the naive approach of applying the readily available least squares algorithm designed for deterministic models. We compare the performance of the recently developed multiple shooting for stochastic systems (MSS) method designed for parameter estimation in stochastic models, a stochastic differential equations based Bayesian approach and a chemical master equation based techniques with the least squares approach for parameter estimation in models of ordinary differential equations (ODE). As test data, 1000 realizations of the stochastic models are simulated. For each realization an estimation is performed with each method, resulting in 1000 estimates for each approach. These are compared with respect to their deviation to the true parameter and, for the genetic toggle switch, also their ability to reproduce the symmetry of the switching behavior. Results are shown for different set of parameter values of a genetic toggle switch leading to symmetric and asymmetric switching behavior as well as an immigration-death and a susceptible-infected-recovered model. This comparison shows that it is important to choose a parameter estimation technique that can treat intrinsic stochasticity and that the specific choice of this algorithm shows only minor performance differences.
Online segmentation of time series based on polynomial least-squares approximations.
Fuchs, Erich; Gruber, Thiemo; Nitschke, Jiri; Sick, Bernhard
2010-12-01
The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the orthogonal expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs.
Linear least squares compartmental-model-independent parameter identification in PET.
Thie, J A; Smith, G T; Hubner, K F
1997-02-01
A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals--all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible.
Extreme Learning Machine and Moving Least Square Regression Based Solar Panel Vision Inspection
Directory of Open Access Journals (Sweden)
Heng Liu
2017-01-01
Full Text Available In recent years, learning based machine intelligence has aroused a lot of attention across science and engineering. Particularly in the field of automatic industry inspection, the machine learning based vision inspection plays a more and more important role in defect identification and feature extraction. Through learning from image samples, many features of industry objects, such as shapes, positions, and orientations angles, can be obtained and then can be well utilized to determine whether there is defect or not. However, the robustness and the quickness are not easily achieved in such inspection way. In this work, for solar panel vision inspection, we present an extreme learning machine (ELM and moving least square regression based approach to identify solder joint defect and detect the panel position. Firstly, histogram peaks distribution (HPD and fractional calculus are applied for image preprocessing. Then an ELM-based defective solder joints identification is discussed in detail. Finally, moving least square regression (MLSR algorithm is introduced for solar panel position determination. Experimental results and comparisons show that the proposed ELM and MLSR based inspection method is efficient not only in detection accuracy but also in processing speed.
Dimension reduction for p53 protein recognition by using incremental partial least squares.
Zeng, Xue-Qiang; Li, Guo-Zheng
2014-06-01
As an important tumor suppressor protein, reactivating mutated p53 was found in many kinds of human cancers and that restoring active p53 would lead to tumor regression. In recent years, more and more data extracted from biophysical simulations, which makes the modelling of mutant p53 transcriptional activity suffering from the problems of huge amount of instances and high feature dimension. Incremental feature extraction is effective to facilitate analysis of large-scale data. However, most current incremental feature extraction methods are not suitable for processing big data with high feature dimension. Partial Least Squares (PLS) has been demonstrated to be an effective dimension reduction technique for classification. In this paper, we design a highly efficient and powerful algorithm named Incremental Partial Least Squares (IPLS), which conducts a two-stage extraction process. In the first stage, the PLS target function is adapted to be incremental with updating historical mean to extract the leading projection direction. In the last stage, the other projection directions are calculated through equivalence between the PLS vectors and the Krylov sequence. We compare IPLS with some state-of-the-arts incremental feature extraction methods like Incremental Principal Component Analysis, Incremental Maximum Margin Criterion and Incremental Inter-class Scatter on real p53 proteins data. Empirical results show IPLS performs better than other methods in terms of balanced classification accuracy.
Least-squares migration of multisource data with a deblurring filter
Dai, Wei
2011-09-01
Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.
Huang, Kang; Wang, Hui-jun; Xu, Hui-rong; Wang, Jian-ping; Ying, Yi-bin
2009-04-01
The application of least square support vector machines (LS-SVM) regression method based on statistics study theory to the analysis with near infrared (NIR) spectra of tomato juice was introduced in the present paper. In this method, LS-SVM was used for establishing model of spectral analysis, and was applied to predict the sugar contents (SC) and available acid (VA) in tomato juice samples. NIR transmission spectra of tomato juice were measured in the spectral range of 800-2,500 nm using InGaAs detector. The radial basis function (RBF) was adopted as a kernel function of LS-SVM. Sixty seven tomato juice samples were used as calibration set, and thirty three samples were used as validation set. The results of the method for sugar contents (SC) and available acid (VA) prediction were: a high correlation coefficient of 0.9903 and 0.9675, and a low root mean square error of prediction (RMSEP) of 0.0056 degree Brix and 0.0245, respectively. And compared to PLS and PCR methods, the performance of the LSSVM method was better. The results indicated that it was possible to built statistic models to quantify some common components in tomato juice using near-infrared (NIR) spectroscopy and least square support vector machines (LS-SVM) regression method as a nonlinear multivariate calibration procedure, and LS-SVM could be a rapid and accurate method for juice components determination based on NIR spectra.
Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems
Energy Technology Data Exchange (ETDEWEB)
Avron, Haim; Ng, Esmond G.; Toledo, Sivan
2008-03-21
We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we can drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.
Multi-loop adaptive internal model control based on a dynamic partial least squares model
Institute of Scientific and Technical Information of China (English)
Zhao ZHAO; Bin HU; Jun LIANG
2011-01-01
A multi-loop adaptive internal model control (IMC) strategy based on a dynamic partial least squares (PLS) framework is proposed to account for plant model errors caused by slow aging, drift in operational conditions, or environmental changes. Since PLS decomposition structure enables multi-loop controller design within latent spaces, a multivariable adaptive control scheme can be converted easily into several independent univariable control loops in the PLS space. In each latent subspace,once the model error exceeds a specific threshold, online adaptation rules are implemented separately to correct the plant model mismatch via a recursive least squares (RLS) algorithm. Because the IMC extracts the inverse of the minimum part of the internal model as its structure, the IMC controller is self-tuned by explicitly updating the parameters, which are parts of the internal model.Both parameter convergence and system stability are briefly analyzed, and proved to be effective. Finally, the proposed control scheme is tested and evaluated using a widely-used benchmark of a multi-input multi-output (MIMO) system with pure delay.
Online Least Squares Estimation with Self-Normalized Processes: An Application to Bandit Problems
Abbasi-Yadkori, Yasin; Szepesvari, Csaba
2011-01-01
The analysis of online least squares estimation is at the heart of many stochastic sequential decision making problems. We employ tools from the self-normalized processes to provide a simple and self-contained proof of a tail bound of a vector-valued martingale. We use the bound to construct a new tighter confidence sets for the least squares estimate. We apply the confidence sets to several online decision problems, such as the multi-armed and the linearly parametrized bandit problems. The confidence sets are potentially applicable to other problems such as sleeping bandits, generalized linear bandits, and other linear control problems. We improve the regret bound of the Upper Confidence Bound (UCB) algorithm of Auer et al. (2002) and show that its regret is with high-probability a problem dependent constant. In the case of linear bandits (Dani et al., 2008), we improve the problem dependent bound in the dimension and number of time steps. Furthermore, as opposed to the previous result, we prove that our bou...
Equalization of Loudspeaker and Room Responses Using Kautz Filters: Direct Least Squares Design
Directory of Open Access Journals (Sweden)
Tuomas Paatero
2007-01-01
Full Text Available DSP-based correction of loudspeaker and room responses is becoming an important part of improving sound reproduction. Such response equalization (EQ is based on using a digital filter in cascade with the reproduction channel to counteract the response errors introduced by loudspeakers and room acoustics. Several FIR and IIR filter design techniques have been proposed for equalization purposes. In this paper we investigate Kautz filters, an interesting class of IIR filters, from the point of view of direct least squares EQ design. Kautz filters can be seen as generalizations of FIR filters and their frequency-warped counterparts. They provide a flexible means to obtain desired frequency resolution behavior, which allows low filter orders even for complex corrections. Kautz filters have also the desirable property to avoid inverting dips in transfer function to sharp and long-ringing resonances in the equalizer. Furthermore, the direct least squares design is applicable to nonminimum-phase EQ design and allows using a desired target response. The proposed method is demonstrated by case examples with measured and synthetic loudspeaker and room responses.
Directory of Open Access Journals (Sweden)
Santosh Kumar Singh
2017-06-01
Full Text Available This paper presents a new hybrid method based on Gravity Search Algorithm (GSA and Recursive Least Square (RLS, known as GSA-RLS, to solve the harmonic estimation problems in the case of time varying power signals in presence of different noises. GSA is based on the Newton’s law of gravity and mass interactions. In the proposed method, the searcher agents are a collection of masses that interact with each other using Newton’s laws of gravity and motion. The basic GSA algorithm strategy is combined with RLS algorithm sequentially in an adaptive way to update the unknown parameters (weights of the harmonic signal. Simulation and practical validation are made with the experimentation of the proposed algorithm with real time data obtained from a heavy paper industry. A comparative performance of the proposed algorithm is evaluated with other recently reported algorithms like, Differential Evolution (DE, Particle Swarm Optimization (PSO, Bacteria Foraging Optimization (BFO, Fuzzy-BFO (F-BFO hybridized with Least Square (LS and BFO hybridized with RLS algorithm, which reveals that the proposed GSA-RLS algorithm is the best in terms of accuracy, convergence and computational time.
Online Least Squares One-Class Support Vector Machines-Based Abnormal Visual Event Detection
Directory of Open Access Journals (Sweden)
Tian Wang
2013-12-01
Full Text Available The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM, combined with its sparsified version (sparse online LS-OC-SVM. LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method.
Two-Stage Orthogonal Least Squares Methods for Neural Network Construction.
Zhang, Long; Li, Kang; Bai, Er-Wei; Irwin, George W
2015-08-01
A number of neural networks can be formulated as the linear-in-the-parameters models. Training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms. Forward selection methods are popular fast subset selection approaches. However, they may only produce suboptimal models and can be trapped into a local minimum. More recently, a two-stage fast recursive algorithm (TSFRA) combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model. This paper proposes unified two-stage orthogonal least squares methods instead of the fast recursive-based methods. In contrast to the TSFRA, this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods. Furthermore, a new term exchanging scheme for backward model refinement is introduced to reduce computational demand. Finally, given the error reduction ratio criterion, effective and efficient forward and backward subset selection procedures are proposed. Extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods.
Nobile, Fabio
2015-01-07
We consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality
Lima, Clodoaldo A M; Coelho, André L V; Eisencraft, Marcio
2010-08-01
The electroencephalogram (EEG) signal captures the electrical activity of the brain and is an important source of information for studying neurological disorders. The proper analysis of this biological signal plays an important role in the domain of brain-computer interface, which aims at the construction of communication channels between human brain and computers. In this paper, we investigate the application of least squares support vector machines (LS-SVM) to the task of epilepsy diagnosis through automatic EEG signal classification. More specifically, we present a sensitivity analysis study by means of which the performance levels exhibited by standard and least squares SVM classifiers are contrasted, taking into account the setting of the kernel function and of its parameter value. Results of experiments conducted over different types of features extracted from a benchmark EEG signal dataset evidence that the sensitivity profiles of the kernel machines are qualitatively similar, both showing notable performance in terms of accuracy and generalization. In addition, the performance accomplished by optimally configured LS-SVM models is also quantitatively contrasted with that obtained by related approaches for the same dataset. Copyright 2010 Elsevier Ltd. All rights reserved.
Iterative methods for mixed finite element equations
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
Mixed finite elements for global tide models
Cotter, Colin J
2014-01-01
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
Radio astronomical image formation using constrained least squares and Krylov subspaces
Mouri Sardarabadi, Ahmad; Leshem, Amir; van der Veen, Alle-Jan
2016-04-01
Aims: Image formation for radio astronomy can be defined as estimating the spatial intensity distribution of celestial sources throughout the sky, given an array of antennas. One of the challenges with image formation is that the problem becomes ill-posed as the number of pixels becomes large. The introduction of constraints that incorporate a priori knowledge is crucial. Methods: In this paper we show that in addition to non-negativity, the magnitude of each pixel in an image is also bounded from above. Indeed, the classical "dirty image" is an upper bound, but a much tighter upper bound can be formed from the data using array processing techniques. This formulates image formation as a least squares optimization problem with inequality constraints. We propose to solve this constrained least squares problem using active set techniques, and the steps needed to implement it are described. It is shown that the least squares part of the problem can be efficiently implemented with Krylov-subspace-based techniques. We also propose a method for correcting for the possible mismatch between source positions and the pixel grid. This correction improves both the detection of sources and their estimated intensities. The performance of these algorithms is evaluated using simulations. Results: Based on parametric modeling of the astronomical data, a new imaging algorithm based on convex optimization, active sets, and Krylov-subspace-based solvers is presented. The relation between the proposed algorithm and sequential source removing techniques is explained, and it gives a better mathematical framework for analyzing existing algorithms. We show that by using the structure of the algorithm, an efficient implementation that allows massive parallelism and storage reduction is feasible. Simulations are used to compare the new algorithm to classical CLEAN. Results illustrate that for a discrete point model, the proposed algorithm is capable of detecting the correct number of sources
Error Estimates Derived from the Data for Least-Squares Spline Fitting
Energy Technology Data Exchange (ETDEWEB)
Jerome Blair
2007-06-25
The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.
Defense of the Least Squares Solution to Peelle’s Pertinent Puzzle
Directory of Open Access Journals (Sweden)
Nicolas Hengartner
2011-02-01
Full Text Available Generalized least squares (GLS for model parameter estimation has a long and successful history dating to its development by Gauss in 1795. Alternatives can outperform GLS in some settings, and alternatives to GLS are sometimes sought when GLS exhibits curious behavior, such as in Peelle’s Pertinent Puzzle (PPP. PPP was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, GLS estimates fell outside the range of the data, eliciting concerns that GLS was somehow flawed. These concerns have led to suggested alternatives to GLS estimators. This paper defends GLS in the PPP context, investigates when PPP can occur, illustrates when PPP can be beneficial for parameter estimation, reviews optimality properties of GLS estimators, and gives an example in which PPP does occur.
Directory of Open Access Journals (Sweden)
Byambaa Dorj
2016-01-01
Full Text Available The next promising key issue of the automobile development is a self-driving technique. One of the challenges for intelligent self-driving includes a lane-detecting and lane-keeping capability for advanced driver assistance systems. This paper introduces an efficient and lane detection method designed based on top view image transformation that converts an image from a front view to a top view space. After the top view image transformation, a Hough transformation technique is integrated by using a parabolic model of a curved lane in order to estimate a parametric model of the lane in the top view space. The parameters of the parabolic model are estimated by utilizing a least-square approach. The experimental results show that the newly proposed lane detection method with the top view transformation is very effective in estimating a sharp and curved lane leading to a precise self-driving capability.
Nonlinear decoupling controller design based on least squares support vector regression
Institute of Scientific and Technical Information of China (English)
WEN Xiang-jun; ZHANG Yu-nong; YAN Wei-wu; XU Xiao-ming
2006-01-01
Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control ora general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is unknown or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.
Generalized total least squares to characterize biogeochemical processes of the ocean
Guglielmi, Véronique; Goyet, Catherine; Touratier, Franck; El Jai, Marie
2016-11-01
The chemical composition of the global ocean is governed by biological, chemical, and physical processes. These processes interact with each other so that the concentrations of carbon, oxygen, nitrogen (mainly from nitrate, nitrite, ammonium), and phosphorous (mainly from phosphate), vary in constant proportions, referred to as the Redfield ratios. We construct here the generalized total least squares estimator of these ratios. The significance of our approach is twofold; it respects the hydrological characteristics of the studied areas, and it can be applied identically in any area where enough data are available. The tests applied to Atlantic Ocean data highlight a variability of the Redfield ratios, both with geographical location and with depth. This variability emphasizes the importance of local and accurate estimates of Redfield ratios.
Partial Least Squares Regression Model to Predict Water Quality in Urban Water Distribution Systems
Institute of Scientific and Technical Information of China (English)
LUO Bijun; ZHAO Yuan; CHEN Kai; ZHAO Xinhua
2009-01-01
The water distribution system of one residential district in Tianjin is taken as an example to analyze the changes of water quality. Partial least squares (PLS) regression model, in which the turbidity and Fe are regarded as con-trol objectives, is used to establish the statistical model. The experimental results indicate that the PLS regression model has good predicted results of water quality compared with the monitored data. The percentages of absolute relative error (below 15%, 20%, 30%) are 44.4%, 66.7%, 100% (turbidity) and 33.3%, 44.4%, 77.8% (Fe) on the 4th sampling point; 77.8%, 88.9%, 88.9% (turbidity) and 44.4%, 55.6%, 66.7% (Fe) on the 5th sampling point.
The Helmholtz equation least squares method for reconstructing and predicting acoustic radiation
Wu, Sean F
2015-01-01
This book gives a comprehensive introduction to the Helmholtz Equation Least Squares (HELS) method and its use in diagnosing noise and vibration problems. In contrast to the traditional NAH technologies, the HELS method does not seek an exact solution to the acoustic field produced by an arbitrarily shaped structure. Rather, it attempts to obtain the best approximation of an acoustic field through the expansion of certain basis functions. Therefore, it significantly simplifies the complexities of the reconstruction process, yet still enables one to acquire an understanding of the root causes of different noise and vibration problems that involve arbitrarily shaped surfaces in non-free space using far fewer measurement points than either Fourier acoustics or BEM based NAH. The examples given in this book illustrate that the HELS method may potentially become a practical and versatile tool for engineers to tackle a variety of complex noise and vibration issues in engineering applications.
Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches.
Hadeler, Karl Peter
2013-01-01
The Michaelis-Menten (MM) function is a fractional linear function depending on two positive parameters. These can be estimated by nonlinear or linear least squares methods. The non-linear methods, based directly on the defect of the MM function, can fail and not produce any minimizer. The linear methods always produce a unique minimizer which, however, may not be positive. Here we give sufficient conditions on the data such that the nonlinear problem has at least one positive minimizer and also conditions for the minimizer of the linear problem to be positive. We discuss in detail the models and equilibrium relations of a classical operator-repressor system, and we extend our approach to the MM problem with leakage and to reversible MM kinetics. The arrangement of the sufficient conditions exhibits the important role of data that have a concavity property (chemically feasible data).
Numerical solution of a nonlinear least squares problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2015-11-01
In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of different incident angles in order to reconstruct a pseudo-3D representation (i.e., a set of 2D slices) of the object. In this paper we describe some mathematical models for polyenergetic digital breast tomosynthesis image reconstruction that explicitly takes into account various materials composing the object and the polyenergetic nature of the x-ray beam. A polyenergetic model helps to reduce beam hardening artifacts, but the disadvantage is that it requires solving a large-scale nonlinear ill-posed inverse problem. We formulate the image reconstruction process (i.e., the method to solve the ill-posed inverse problem) in a nonlinear least squares framework, and use a Levenberg-Marquardt scheme to solve it. Some implementation details are discussed, and numerical experiments are provided to illustrate the performance of the methods.
Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application
Institute of Scientific and Technical Information of China (English)
JIA Jin-ming; WEN Xiang-jun
2008-01-01
Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the iuner-product kernel spanned by the spline basis functions with infinite numher of nodes,this method firstly maps the input data into a high dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS"kernel"algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input (primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.
Least Squares Temporal Difference Actor-Critic Methods with Applications to Robot Motion Control
Estanjini, Reza Moazzez; Lahijanian, Morteza; Wang, Jing; Belta, Calin A; Paschalidis, Ioannis Ch
2011-01-01
We consider the problem of finding a control policy for a Markov Decision Process (MDP) to maximize the probability of reaching some states while avoiding some other states. This problem is motivated by applications in robotics, where such problems naturally arise when probabilistic models of robot motion are required to satisfy temporal logic task specifications. We transform this problem into a Stochastic Shortest Path (SSP) problem and develop a new approximate dynamic programming algorithm to solve it. This algorithm is of the actor-critic type and uses a least-square temporal difference learning method. It operates on sample paths of the system and optimizes the policy within a pre-specified class parameterized by a parsimonious set of parameters. We show its convergence to a policy corresponding to a stationary point in the parameters' space. Simulation results confirm the effectiveness of the proposed solution.
Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
Marichal, Jean-Luc
2012-01-01
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified degree. We first observe that this property still holds if we consider approximations by pseudo-Boolean functions depending only on specified variables. We then show that the Banzhaf influence index can also be obtained from the latter approximation problem. Considering certain weighted versions of this approximation problem, we introduce a class of weighted Banzhaf influence indexes, analyze their most important properties, and point out similarities between the weighted Banzhaf influence index and the corresponding weighted Banzhaf interaction index.
Xu, Lin; Feng, Yanqiu; Liu, Xiaoyun; Kang, Lili; Chen, Wufan
2014-01-01
Accuracy of interpolation coefficients fitting to the auto-calibrating signal data is crucial for k-space-based parallel reconstruction. Both conventional generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction that utilizes linear interpolation function and nonlinear GRAPPA (NLGRAPPA) reconstruction with polynomial kernel function are sensitive to interpolation window and often cannot consistently produce good results for overall acceleration factors. In this study, sparse multi-kernel learning is conducted within the framework of least squares support vector regression to fit interpolation coefficients as well as to reconstruct images robustly under different subsampling patterns and coil datasets. The kernel combination weights and interpolation coefficients are adaptively determined by efficient semi-infinite linear programming techniques. Experimental results on phantom and in vivo data indicate that the proposed method can automatically achieve an optimized compromise between noise suppression and residual artifacts for various sampling schemes. Compared with NLGRAPPA, our method is significantly less sensitive to the interpolation window and kernel parameters.
Baseline configuration for GNSS attitude determination with an analytical least-squares solution
Chang, Guobin; Xu, Tianhe; Wang, Qianxin
2016-12-01
The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance-covariance matrix.
Novel passive localization algorithm based on double side matrix-restricted total least squares
Institute of Scientific and Technical Information of China (English)
Xu Zheng; Qu Changwen; Wang Changhai
2013-01-01
In order to solve the bearings-only passive localization problem in the presence of erroneous observer position,a novel algorithm based on double side matrix-restricted total least squares (DSMRTLS) is proposed.First,the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector.Second,the corresponding optimization problem of the DSMRTLS problem without constraint is derived,which can be approximated as the generalized Rayleigh quotient minimization problem.Then,the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition.Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms.
Recursive N-way partial least squares for brain-computer interface.
Directory of Open Access Journals (Sweden)
Andrey Eliseyev
Full Text Available In the article tensor-input/tensor-output blockwise Recursive N-way Partial Least Squares (RNPLS regression is considered. It combines the multi-way tensors decomposition with a consecutive calculation scheme and allows blockwise treatment of tensor data arrays with huge dimensions, as well as the adaptive modeling of time-dependent processes with tensor variables. In the article the numerical study of the algorithm is undertaken. The RNPLS algorithm demonstrates fast and stable convergence of regression coefficients. Applied to Brain Computer Interface system calibration, the algorithm provides an efficient adjustment of the decoding model. Combining the online adaptation with easy interpretation of results, the method can be effectively applied in a variety of multi-modal neural activity flow modeling tasks.
Concerning an application of the method of least squares with a variable weight matrix
Sukhanov, A. A.
1979-01-01
An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.
Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design
Directory of Open Access Journals (Sweden)
Lo-Chyuan Su
2013-01-01
Full Text Available All-pass filter design can be generally achieved by solving a system of linear equations. The associated matrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition technique. In this paper, based on trigonometric identities and sampling the frequency band of interest uniformly, the authors proposed closed-form expressions to compute the elements of the Toeplitz-plus-Hankel matrix required in the least-squares design of IIR all-pass filters. Simulation results confirm that the proposed method achieves good performance as well as effectiveness.
Directory of Open Access Journals (Sweden)
Ibrahim Mohd Tarmizi
2017-01-01
Full Text Available Theories are developed to explain an observed phenomenon in an effort to understand why and how things happen. Theories thus, use latent variables to estimate conceptual parameters. The level of abstraction depends, partly on the complexity of the theoretical model explaining the phenomenon. The conjugation of directly-measured variables leads to a formation of a first-order factor. A combination of theoretical underpinnings supporting an existence of a higher-order components, and statistical evidence pointing to such presence adds advantage for the researchers to investigate a phenomenon both at an aggregated and disjointed dimensions. As partial least square (PLS gains its tractions in theory development, behavioural accounting discipline in general should exploit the flexibility of PLS to work with the higher-order factors. However, technical guides are scarcely available. Therefore, this article presents a PLS approach to validate a higher-order factor on a statistical ground using accounting information system dataset.
DEFF Research Database (Denmark)
Garcia, Emanuel; Klaas, Ilka Christine; Amigo Rubio, Jose Manuel;
2014-01-01
. Eighty variables retrieved from AMS were summarized week-wise and used to predict 2 defined classes: nonlame and clinically lame cows. Variables were represented with 2 transformations of the week summarized variables, using 2-wk data blocks before gait scoring, totaling 320 variables (2 × 2 × 80......). The reference gait scoring error was estimated in the first week of the study and was, on average, 15%. Two partial least squares discriminant analysis models were fitted to parity 1 and parity 2 groups, respectively, to assign the lameness class according to the predicted probability of being lame (score 3......Lameness is prevalent in dairy herds. It causes decreased animal welfare and leads to higher production costs. This study explored data from an automatic milking system (AMS) to model on-farm gait scoring from a commercial farm. A total of 88 cows were gait scored once per week, for 2 5-wk periods...
Spline based least squares integration for two-dimensional shape or wavefront reconstruction
Huang, Lei; Xue, Junpeng; Gao, Bo; Zuo, Chao; Idir, Mourad
2017-04-01
In this work, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. The noise influence is studied by adding white Gaussian noise to the slope data. Experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.
Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding
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Ying Chen
2014-05-01
Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.
Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil
Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris
2016-01-01
Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.
Directory of Open Access Journals (Sweden)
Margaretha Ohyver
2014-12-01
Full Text Available Multicollinearity and outliers are the common problems when estimating regression model. Multicollinearitiy occurs when there are high correlations among predictor variables, leading to difficulties in separating the effects of each independent variable on the response variable. While, if outliers are present in the data to be analyzed, then the assumption of normality in the regression will be violated and the results of the analysis may be incorrect or misleading. Both of these cases occurred in the data on room occupancy rate of hotels in Kendari. The purpose of this study is to find a model for the data that is free of multicollinearity and outliers and to determine the factors that affect the level of room occupancy hotels in Kendari. The method used is Continuous Wavelet Transformation and Partial Least Squares. The result of this research is a regression model that is free of multicollinearity and a pattern of data that resolved the present of outliers.
Institute of Scientific and Technical Information of China (English)
Juan ZHAO; Yunmin ZHU
2009-01-01
The optimally weighted least squares estimate and the linear minimum variance estimate are two of the most popular estimation methods for a linear model. In this paper, the authors make a comprehensive discussion about the relationship between the two estimates. Firstly, the authors consider the classical linear model in which the coefficient matrix of the linear model is deterministic,and the necessary and sufficient condition for equivalence of the two estimates is derived. Moreover,under certain conditions on variance matrix invertibility, the two estimates can be identical provided that they use the same a priori information of the parameter being estimated. Secondly, the authors consider the linear model with random coefficient matrix which is called the extended linear model;under certain conditions on variance matrix invertibility, it is proved that the former outperforms the latter when using the same a priori information of the parameter.
Water Quantity Prediction Using Least Squares Support Vector Machines (LS-SVM Method
Directory of Open Access Journals (Sweden)
Nian Zhang
2014-08-01
Full Text Available The impact of reliable estimation of stream flows at highly urbanized areas and the associated receiving waters is very important for water resources analysis and design. We used the least squares support vector machine (LS-SVM based algorithm to forecast the future streamflow discharge. A Gaussian Radial Basis Function (RBF kernel framework was built on the data set to optimize the tuning parameters and to obtain the moderated output. The training process of LS-SVM was designed to select both kernel parameters and regularization constants. The USGS real-time water data were used as time series input. 50% of the data were used for training, and 50% were used for testing. The experimental results showed that the LS-SVM algorithm is a reliable and efficient method for streamflow prediction, which has an important impact to the water resource management field.
Directory of Open Access Journals (Sweden)
Saïda Bedoui
2013-01-01
Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
Joint cluster and non-negative least squares analysis for aerosol mass spectrum data
Energy Technology Data Exchange (ETDEWEB)
Zhang, T; Zhu, W [Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600 (United States); McGraw, R [Environmental Sciences Department, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States)], E-mail: zhu@ams.sunysb.edu
2008-07-15
Aerosol mass spectrum (AMS) data contain hundreds of mass to charge ratios and their corresponding intensities from air collected through the mass spectrometer. The observations are usually taken sequentially in time to monitor the air composition, quality and temporal change in an area of interest. An important goal of AMS data analysis is to reduce the dimensionality of the original data yielding a small set of representing tracers for various atmospheric and climatic models. In this work, we present an approach to jointly apply the cluster analysis and the non-negative least squares method towards this goal. Application to a relevant study demonstrates the effectiveness of this new approach. Comparisons are made to other relevant multivariate statistical techniques including the principal component analysis and the positive matrix factorization method, and guidelines are provided.
Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction.
Gregor, Jens; Fessler, Jeffrey A
2015-03-01
Tomographic image reconstruction is often formulated as a regularized weighted least squares (RWLS) problem optimized by iterative algorithms that are either inherently algebraic or derived from a statistical point of view. This paper compares a modified version of SIRT (Simultaneous Iterative Reconstruction Technique), which is of the former type, with a version of SQS (Separable Quadratic Surrogates), which is of the latter type. We show that the two algorithms minimize the same criterion function using similar forms of preconditioned gradient descent. We present near-optimal relaxation for both based on eigenvalue bounds and include a heuristic extension for use with ordered subsets. We provide empirical evidence that SIRT and SQS converge at the same rate for all intents and purposes. For context, we compare their performance with an implementation of preconditioned conjugate gradient. The illustrative application is X-ray CT of luggage for aviation security.
Kazemi, Mahdi; Arefi, Mohammad Mehdi
2016-12-15
In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.
Prediction of chaotic systems with multidimensional recurrent least squares support vector machines
Institute of Scientific and Technical Information of China (English)
Sun Jian-Cheng; Zhou Ya-Tong; Luo Jian-Guo
2006-01-01
In this paper, we propose a multidimensional version of recurrent least squares support vector machines (MDRLSSVM) to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens's embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the highdimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.
Continuity constrained least-squares interpolation for SFO suppression in immersed boundary methods
Martins, Diogo M. C.; Albuquerque, Duarte M. S.; Pereira, José C. F.
2017-05-01
A new immersed boundary interpolation for discrete forcing methods is presented. The method decreases spurious oscillations in the pressure field and consequently in the body force calculations which are a common issue in several immersed boundary methods. The method applies a continuity constraint in the least-squares interpolation, and guarantees that adjacent interpolation polynomials are continuous between each other. This approach strictly enforces continuity in the flow reconstruction domain, reducing time discontinuities caused by the boundary conditions applied at the immersed boundary. Several moving body problems test cases are simulated, including a three dimensional one, to demonstrate the new method's capability of computing stable pressure fields, even for coarse grids and small CFL numbers, which are known to increase the pressure oscillations.
On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships
Institute of Scientific and Technical Information of China (English)
Irinel DRAGAN
2006-01-01
In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done.
Dutta, Saibal; Chatterjee, Amitava; Munshi, Sugata
2010-12-01
The present work proposes the development of an automated medical diagnostic tool that can classify ECG beats. This is considered an important problem as accurate, timely detection of cardiac arrhythmia can help to provide proper medical attention to cure/reduce the ailment. The proposed scheme utilizes a cross-correlation based approach where the cross-spectral density information in frequency domain is used to extract suitable features. A least square support vector machine (LS-SVM) classifier is developed utilizing the features so that the ECG beats are classified into three categories: normal beats, PVC beats and other beats. This three-class classification scheme is developed utilizing a small training dataset and tested with an enormous testing dataset to show the generalization capability of the scheme. The scheme, when employed for 40 files in the MIT/BIH arrhythmia database, could produce high classification accuracy in the range 95.51-96.12% and could outperform several competing algorithms.
Li, Wen-Tao; Huang, Lin-Fang; Du, Jing; Chen, Shi-Lin
2013-10-01
A total of eleven ecological factors values were obtained from the ecological suitability database of the geographic information system for traditional Chinese medicines production areas (TCM-GIS), and the relationships between the chemical components of Dendrobium and the ecological factors were analyzed by partial least square (PLS) regression. There existed significant differences in the chemical components contents of the same species of Dendrobium in different areas. The polysaccharides content of D. officinale had significant positive correlation with soil type, the accumulated dendrobine in D. nobile was significantly positively correlated with annual precipitation, and the erianin content of D. chrysotoxum was mainly affected by air temperature. The principal component analysis (PCA) showed that Zhejiang Province was the optimal production area for D. officinale, Guizhou Province was the most appropriate planting area for D. nobile, and Yunnan Province was the best production area of D. chrysotoxum.
Experiments using least square lattice filters for the identification of structural dynamics
Sundararajan, N.; Montgomery, R. C.
1983-01-01
An approach for identifying the dynamics of large space structures is applied to a free-free beam. In this approach the system's order is determined on-line, along with mode shapes, using recursive lattice filters which provide a least square estimate of the measurement data. The mode shapes determined are orthonormal in the space of the measurements and, hence, are not the natural modes of the structure. To determine the natural modes of the structure, a method based on the fast Fourier transform is used on the outputs of the lattice filter. These natural modes are used to obtain the modal amplitude time series which provides the input data for an output error parameter identification scheme that identifies the ARMA parameters of the difference equation model of the modes. the approach is applied to both simulated and experimental data.
Yin, Zhong; Zhang, Jianhua
2014-01-01
This paper proposed two psychophysiological-data-driven classification frameworks for operator functional states (OFS) assessment in safety-critical human-machine systems with stable generalization ability. The recursive feature elimination (RFE) and least square support vector machine (LSSVM) are combined and used for binary and multiclass feature selection. Besides typical binary LSSVM classifiers for two-class OFS assessment, two multiclass classifiers based on multiclass LSSVM-RFE and decision directed acyclic graph (DDAG) scheme are developed, one used for recognizing the high mental workload and fatigued state while the other for differentiating overloaded and base-line states from the normal states. Feature selection results have revealed that different dimensions of OFS can be characterized by specific set of psychophysiological features. Performance comparison studies show that reasonable high and stable classification accuracy of both classification frameworks can be achieved if the RFE procedure is properly implemented and utilized.
Adaptive control of a flexible beam using least square lattice filters
Sundararajan, N.; Montgomery, R. C.
1983-01-01
This paper presents an indirect adaptive control scheme for the control of flexible structures using recursive least square lattice filters. The identification scheme uses lattice filters which provide an on-line estimate of the number of modes, mode shapes and modal amplitudes. These modes are coupled and a transformation to decouple them in order to obtain the natural modes is presented. The decoupled modal amplitude time series are then used in an equation error identification scheme to identify the model parameters in an autoregressive moving average (ARMA) form. The control is based on modal pole placement scheme with the objective of vibration suppression. The control gains are calculated based on the identified ARMA parameters. Before using the identified parameters for control, detailed testing and validation procedures are carried out on the identified parameters. The full adaptive control scheme is demonstrated using the simulation for the 12 foot free-free beam apparatus at NASA Langley Research Center.
Energy Technology Data Exchange (ETDEWEB)
Clegg, Samuel M [Los Alamos National Laboratory; Barefield, James E [Los Alamos National Laboratory; Wiens, Roger C [Los Alamos National Laboratory; Sklute, Elizabeth [MT HOLYOKE COLLEGE; Dyare, Melinda D [MT HOLYOKE COLLEGE
2008-01-01
Quantitative analysis with LIBS traditionally employs calibration curves that are complicated by the chemical matrix effects. These chemical matrix effects influence the LIBS plasma and the ratio of elemental composition to elemental emission line intensity. Consequently, LIBS calibration typically requires a priori knowledge of the unknown, in order for a series of calibration standards similar to the unknown to be employed. In this paper, three new Multivariate Analysis (MV A) techniques are employed to analyze the LIBS spectra of 18 disparate igneous and highly-metamorphosed rock samples. Partial Least Squares (PLS) analysis is used to generate a calibration model from which unknown samples can be analyzed. Principal Components Analysis (PCA) and Soft Independent Modeling of Class Analogy (SIMCA) are employed to generate a model and predict the rock type of the samples. These MV A techniques appear to exploit the matrix effects associated with the chemistries of these 18 samples.
Song, Jun-Ling; Hong, Yan-Ji; Wang, Guang-Yu; Pan, Hu
2013-08-01
The measurement of nonuniform temperature and concentration distributions was investigated based on tunable diode laser absorption spectroscopy technology. Through direct scanning multiple absorption lines of H2O, two zones for temperature and concentration distribution were achieved by solving nonlinear equations by least-square fitting from numerical and experimental studies. The numerical results show that the calculated temperature and concentration have relative errors of 8.3% and 7.6% compared to the model, respectively. The calculating accuracy can be improved by increasing the number of absorption lines and reduction in unknown numbers. Compared with the thermocouple readings, the high and low temperatures have relative errors of 13.8% and 3.5% respectively. The numerical results are in agreement with the experimental results.
On-line least squares support vector machine algorithm in gas prediction
Institute of Scientific and Technical Information of China (English)
ZHAO Xiao-hu; WANG Gang; ZHAO Ke-ke; TAN De-jian
2009-01-01
Traditional coal mine safety prediction methods are off-line and do not have dynamic prediction functions. The Support Vector Machine (SVM) is a new machine learning algorithm that has excellent properties. The least squares support vector machine (LS-SVM) algorithm is an improved algorithm of SVM. But the common LS-SVM algorithm, used directly in safety predictions, has some problems. We have first studied gas prediction problems and the basic theory of LS-SVM. Given these problems, we have investigated the affect of the time factor about safety prediction and present an on-line prediction algorithm, based on LS-SVM. Finally, given our observed data, we used the on-line algorithm to predict gas emissions and used other related algorithm to com- pare its performance. The simulation results have verified the validity of the new algorithm.
A Selective Moving Window Partial Least Squares Method and Its Application in Process Modeling
Institute of Scientific and Technical Information of China (English)
Ouguan Xu; Yongfeng Fu; Hongye Su; Lijuan Li
2014-01-01
A selective moving window partial least squares (SMW-PLS) soft sensor was proposed in this paper and applied to a hydro-isomerization process for on-line estimation of para-xylene (PX) content. Aiming at the high frequen-cy of model updating in previous recursive PLS methods, a selective updating strategy was developed. The model adaptation is activated once the prediction error is larger than a preset threshold, or the model is kept unchanged. As a result, the frequency of model updating is reduced greatly, while the change of prediction accuracy is minor. The performance of the proposed model is better as compared with that of other PLS-based model. The compro-mise between prediction accuracy and real-time performance can be obtained by regulating the threshold. The guidelines to determine the model parameters are illustrated. In summary, the proposed SMW-PLS method can deal with the slow time-varying processes effectively.
A hybrid least squares support vector machines and GMDH approach for river flow forecasting
Samsudin, R.; Saad, P.; Shabri, A.
2010-06-01
This paper proposes a novel hybrid forecasting model, which combines the group method of data handling (GMDH) and the least squares support vector machine (LSSVM), known as GLSSVM. The GMDH is used to determine the useful input variables for LSSVM model and the LSSVM model which works as time series forecasting. In this study the application of GLSSVM for monthly river flow forecasting of Selangor and Bernam River are investigated. The results of the proposed GLSSVM approach are compared with the conventional artificial neural network (ANN) models, Autoregressive Integrated Moving Average (ARIMA) model, GMDH and LSSVM models using the long term observations of monthly river flow discharge. The standard statistical, the root mean square error (RMSE) and coefficient of correlation (R) are employed to evaluate the performance of various models developed. Experiment result indicates that the hybrid model was powerful tools to model discharge time series and can be applied successfully in complex hydrological modeling.