The Experts below are selected from a list of 4632 Experts worldwide ranked by ideXlab platform
Yiyuan She - One of the best experts on this subject based on the ideXlab platform.
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robust Orthogonal Complement principal component analysis
Journal of the American Statistical Association, 2016Co-Authors: Yiyuan SheAbstract:AbstractRecently, the robustification of principal component analysis (PCA) has attracted lots of attention from statisticians, engineers, and computer scientists. In this work, we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust Orthogonal Complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low-rank regularization techniques to deal with row-wise outliers as well as element-wise outliers. A nonasymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. Th...
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robust Orthogonal Complement principal component analysis
arXiv: Methodology, 2014Co-Authors: Yiyuan SheAbstract:Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust Orthogonal Complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low rank regularization techniques to deal with row-wise outliers as well as element-wise outliers. A non-asymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. The paper also points out a pitfall of a common practice of SVD reduction in robust PCA. Experiments show the effectiveness and efficiency of ROC-PCA in both synthetic and real data.
Isao Yamada - One of the best experts on this subject based on the ideXlab platform.
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Smoothing of adaptive eigenvector extraction in nested Orthogonal Complement structure with minimum disturbance principle
Multidimensional Systems and Signal Processing, 2017Co-Authors: Kenji Kakimoto, Masao Yamagishi, Isao YamadaAbstract:For adaptive extraction of generalized eigensubspace, Nguyen, Takahashi and Yamada proposed a scheme for solving generalized Hermitian eigenvalue problem based on nested Orthogonal Complement structure. This scheme can extract multiple generalized eigenvectors by combining with any algorithm designed for estimation of the first minor generalized eigenvector. In this paper, we carefully analyse the effect of a discontinuous function employed in the scheme, and show that the discontinuous function can cause unsmooth changes of the estimates by the scheme in its adaptive implementation. To remedy the weakness, we newly introduce a projection step, for smoothing, without increasing the order of the computational complexity. Numerical experiments show that the learning curves of the non-first generalized eigenvectors are improved drastically through the proposed smoothing even when the original scheme results in unexpected performance degradation.
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stabilization of adaptive eigenvector extraction by continuation in nested Orthogonal Complement structure
International Conference on Acoustics Speech and Signal Processing, 2016Co-Authors: Kenji Kakimoto, Masao Yamagishi, Daichi Kitahara, Isao YamadaAbstract:Nguyen and Yamada [NY'13] proposed an adaptive algorithm for fast and stable extraction of the first generalized Hermitian eigenvector and mentioned the extension to the first r generalized eigenvector extraction based on the nested Orthogonal Complement structure [NTY'12]. However, we recently found that the estimates of the eigenvectors are not expressed ideally in the time-varying coordinate system and can change drastically in a certain situation, which may cause numerical instability. In this paper, we propose a new expression of the estimates along with time-varying coordinate system. This modification can be done efficiently with additional multiplications of Orthogonal Complement matrices. Numerical experiments show that the modified scheme has better stability compared with the original scheme [NTY'12].
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An adaptive extraction of generalized eigensubspace by using exact nested Orthogonal Complement structure
Multidimensional Systems and Signal Processing, 2013Co-Authors: Tuan Duong Nguyen, Noriyuki Takahashi, Isao YamadaAbstract:The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The key of this scheme is the reduction of the problem for extracting the i th ( i ≥ 2) minor generalized eigenvector of the original matrix pencil to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector. Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace. Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms.
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an efficient adaptive minor subspace extraction using exact nested Orthogonal Complement structure
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2008Co-Authors: Masaki Misono, Isao YamadaAbstract:This paper presents a new adaptive minor subspace extraction algorithm based on an idea of Peng and Yi ('07) for approximating the single minor eigenvector of a covariance matrix. By utilizing the idea inductively in the nested Orthogonal Complement subspaces, the proposed algorithm succeeds to relax the numerical sensitivity which has been annoying conventional adaptive minor subspace extraction algorithms for example, Oja algorithm ('82) and its stabilized version: O-Oja algorithm ('02). Simulation results demonstrate that the proposed algorithm realizes more stable convergence than O-Oja algorithm.
Lei Wang - One of the best experts on this subject based on the ideXlab platform.
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npsa nonOrthogonal principal skewness analysis
IEEE Transactions on Image Processing, 2020Co-Authors: Xiurui Geng, Lei WangAbstract:Principal skewness analysis (PSA) has been introduced for feature extraction in hyperspectral imagery. As a third-order generalization of principal component analysis (PCA), its solution of searching for the local maximum skewness direction is transformed into the problem of calculating the eigenpairs (the eigenvalues and the corresponding eigenvectors) of a coskewness tensor. By combining a fixed-point method with an Orthogonal constraint, the new eigenpairs are prevented from converging to the same previously determined maxima. However, in general, the eigenvectors of the supersymmetric tensor are not inherently Orthogonal, which implies that the results obtained by the search strategy used in PSA may unavoidably deviate from the actual eigenpairs. In this paper, we propose a new nonOrthogonal search strategy to solve this problem and the new algorithm is named nonOrthogonal principal skewness analysis (NPSA). The contribution of NPSA lies in the finding that the search space of the eigenvector to be determined can be enlarged by using the Orthogonal Complement of the Kronecker product of the previous eigenvector with itself, instead of its Orthogonal Complement space. We also give a detailed theoretical proof on why we can obtain the more accurate eigenpairs through the new search strategy by comparison with PSA. In addition, after some algebraic derivations, the complexity of the presented algorithm is also greatly reduced. Experiments with both simulated data and real multi/hyperspectral imagery demonstrate its validity in feature extraction.
Kurt S Anderson - One of the best experts on this subject based on the ideXlab platform.
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performance investigation and constraint stabilization approach for the Orthogonal Complement based divide and conquer algorithm
Mechanism and Machine Theory, 2013Co-Authors: Imad M Khan, Kurt S AndersonAbstract:Abstract The introductory paper on the Orthogonal Complement-based divide-and-conquer algorithm (ODCA) lacked in properly characterizing the growth rate of the constraint violation error and the singularity handling capabilities of the algorithm [1] . In this paper, we investigate the performance of the ODCA with regards to constraint error growth and singularity handling capabilities. Moreover we introduce a new inverse dynamics-based constraint stabilization approach. The proposed method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the ODCA with augmented [2] and reduction [3] methods. Our results indicate that the error growth rate for the ODCA falls between these two traditional techniques. Moreover, using benchmark numerical problems, we illustrate the effectiveness of the stabilization scheme.
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Orthogonal Complement based divide and conquer algorithm a detailed investigation of its performance
ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2013Co-Authors: Imad M Khan, Kurt S AndersonAbstract:In this paper, we characterize the Orthogonal Complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.Copyright © 2013 by ASME
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generalized Orthogonal Complement based divide and conquer algorithm for constrained multibody dynamics
ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2009Co-Authors: Rudranarayan Mukherjee, Kurt S AndersonAbstract:This paper presents an extension of the Orthogonal Complement based divide and conquer algorithm for constraint multi-rigid body systems containing closed kinematic loops in generalized topologies. In its current form, its a short article demonstrating the methodology for assembling the equations of motion in a hierarchic assembly process for systems containing multiple loops in generalized topologies.Copyright © 2009 by ASME
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Orthogonal Complement based divide and conquer algorithm for constrained multibody systems
Nonlinear Dynamics, 2007Co-Authors: Rudranarayan M Mukherjee, Kurt S AndersonAbstract:A new algorithm, Orthogonal Complement based Divide-and-Conquer Algorithm (O-DCA), is presented in this paper for calculating the forward dynamics of constrained multi-rigid bodies including topologies involving single or coupled closed kinematic loops. The algorithm is exact and noniterative. The constraints are imposed at the acceleration level by utilizing a kinematic relation between the joint motion subspace (or partial velocities) and its Orthogonal Complement. Sample test cases indicate excellent constraint satisfaction and robust handling of singular configurations. Since the present algorithm does not use either a reduction or augmentation approach in the traditional sense for imposing the constraints, it does not suffer from the associated problems for systems passing through singular configurations. The computational complexity of the algorithm is expected to be O(n+m) and O(log(n+m)) for serial and parallel implementation, respectively, where n is the number of generalized coordinates and m is the number of independent algebraic constraints.
Xiurui Geng - One of the best experts on this subject based on the ideXlab platform.
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npsa nonOrthogonal principal skewness analysis
IEEE Transactions on Image Processing, 2020Co-Authors: Xiurui Geng, Lei WangAbstract:Principal skewness analysis (PSA) has been introduced for feature extraction in hyperspectral imagery. As a third-order generalization of principal component analysis (PCA), its solution of searching for the local maximum skewness direction is transformed into the problem of calculating the eigenpairs (the eigenvalues and the corresponding eigenvectors) of a coskewness tensor. By combining a fixed-point method with an Orthogonal constraint, the new eigenpairs are prevented from converging to the same previously determined maxima. However, in general, the eigenvectors of the supersymmetric tensor are not inherently Orthogonal, which implies that the results obtained by the search strategy used in PSA may unavoidably deviate from the actual eigenpairs. In this paper, we propose a new nonOrthogonal search strategy to solve this problem and the new algorithm is named nonOrthogonal principal skewness analysis (NPSA). The contribution of NPSA lies in the finding that the search space of the eigenvector to be determined can be enlarged by using the Orthogonal Complement of the Kronecker product of the previous eigenvector with itself, instead of its Orthogonal Complement space. We also give a detailed theoretical proof on why we can obtain the more accurate eigenpairs through the new search strategy by comparison with PSA. In addition, after some algebraic derivations, the complexity of the presented algorithm is also greatly reduced. Experiments with both simulated data and real multi/hyperspectral imagery demonstrate its validity in feature extraction.
