THE COMPUTATION OF LOW MULTILINEAR RANK APPROXIMATIONS OF TENSORS VIA POWER SCHEME AND RANDOM PROJECTION

被引：31

作者：

Che, Maolin ^{[1
]}

Wei, Yimin ^{[2
,3
]}

Yan, Hong ^{[4
]}

机构：

[1] Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 611130, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

[4] City Univ Hong Kong, Dept Elect Engn, Kowloon, 83 Tat Chee Ave, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2020年 / 41卷 / 02期

基金：

中国国家自然科学基金;

关键词：

randomized algorithms; random projection; low multilinear rank approximation; random sub-Gaussian matrices; power scheme; singular values; singular value decomposition; SMALLEST SINGULAR-VALUE; ALGORITHMS; TUCKER; DECOMPOSITION; FACTORIZATIONS; REDUCTION;

D O I：

10.1137/19M1237016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the computation of low multilinear rank approximations of tensors. Combining the stretegy of power scheme, random projection, and singular value decomposition, we derive a three-stage randomized algorithm for the low multilinear rank approximation. Based on the singular values of sub-Gaussian matrices, we derive the error bound of the proposed algorithm with high probability. We illustrate the proposed algorithms via several numerical examples.

引用

页码：605 / 636

页数：32

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