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A Robust Canonical Polyadic Tensor Decomposition via Structured Low-Rank Matrix Approximation

Riku AKEMA, Masao YAMAGISHI, Isao YAMADA

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Summary :

The Canonical Polyadic Decomposition (CPD) is the tensor analog of the Singular Value Decomposition (SVD) for a matrix and has many data science applications including signal processing and machine learning. For the CPD, the Alternating Least Squares (ALS) algorithm has been used extensively. Although the ALS algorithm is simple, it is sensitive to a noise of a data tensor in the applications. In this paper, we propose a novel strategy to realize the noise suppression for the CPD. The proposed strategy is decomposed into two steps: (Step 1) denoising the given tensor and (Step 2) solving the exact CPD of the denoised tensor. Step 1 can be realized by solving a structured low-rank approximation with the Douglas-Rachford splitting algorithm and then Step 2 can be realized by solving the simultaneous diagonalization of a matrix tuple constructed by the denoised tensor with the DODO method. Numerical experiments show that the proposed algorithm works well even in typical cases where the ALS algorithm suffers from the so-called bottleneck/swamp effect.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.1 pp.11-24
Publication Date
2022/01/01
Publicized
2021/06/23
Online ISSN
1745-1337
DOI
10.1587/transfun.2020EAP1138
Type of Manuscript
PAPER
Category
Digital Signal Processing

Authors

Riku AKEMA
  Tokyo Institute of Technology
Masao YAMAGISHI
  Tokyo Institute of Technology
Isao YAMADA
  Tokyo Institute of Technology

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