The Exact Solution to Rank-1 L1-Norm TUCKER2 Decomposition

被引：19

作者：

Markopoulos, Panos P. ^{[1
]}

Chachlakis, Dimitris G. ^{[1
]}

Papalexakis, Evangelos E. ^{[2
]}

机构：

[1] Rochester Inst Technol, Dept Elect & Microelect Engn, Rochester, NY 14623 USA

[2] Univ Calif Riverside, Dept Comp Sci & Engn, Riverside, CA 92521 USA

来源：

IEEE SIGNAL PROCESSING LETTERS | 2018年 / 25卷 / 04期

关键词：

Data analysis; L1-norm; outliers; robust; tensors; TUCKER decomposition; TENSOR DECOMPOSITIONS; APPROXIMATIONS; ALGORITHMS;

D O I：

10.1109/LSP.2018.2790901

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

This letter studies the rank-1 L1-norm-based TUCKER2 (L1-TUCKER2) decomposition of 3-way tensors. First, we prove that the problem is formally NP-hard. Then, we derive the first two algorithms in the literature for its exact solution. Our algorithms are accompanied by formal complexity analysis. Finally, we conduct numerical studies to compare the performance of exact L1-TUCKER2 (proposed) with standard HOSVD, HOOI, GLRAM, PCA, L1-PCA, and TPCA-L1. In our numerical studies, L1-TUCKER2 outperforms (e.g., in tensor approximation) all the aforementioned counterparts when the processed data are outlier corrupted.

引用

页码：511 / 515

页数：5

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