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
收藏
页码：605 / 636
页数：32
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