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Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

XIN LIU (liuxin***at***lsec.cc.ac.cn)
ZAIWEN WEN (zw2109***at***sjtu.edu.cn)
YIN ZHANG (yzhang***at***rice.edu)

Abstract: In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations often require efficiently, reliably and accurately computing dominant singular value decompositions (SVDs) of large unstructured matrices. In this paper, we propose and study a subspace optimization technique to significantly accelerate the classic simultaneous iteration method. We analyze the convergence of the proposed algorithm, and numerically compare it with several state-of-the-art SVD solvers under the MATLAB environment. Extensive computational results show that on a wide range of large unstructured matrices, the proposed algorithm can often provide improved efficiency or robustness over existing algorithms.

Keywords: subspace optimization, dominant singular value decomposition, Krylov subspace, eigenvalue decomposition

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Applications -- Science and Engineering (Data-Mining )

Citation:

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Entry Submitted: 03/22/2012
Entry Accepted: 03/22/2012
Entry Last Modified: 03/23/2012

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