Canonical Polyadic Tensor Decomposition With Low-Rank Factor Matrices

Anh-Huy Phan; Petr Tichavský; Konstantin Sobolev; Konstantin Sozykin; Dmitry Ermilov; Andrzej Cichocki

ICASSP 2021accepted0 citations

Canonical Polyadic Tensor Decomposition With Low-Rank Factor Matrices

Anh-Huy Phan, Petr Tichavský, Konstantin Sobolev, Konstantin Sozykin, Dmitry Ermilov, Andrzej Cichocki

Abstract

This paper proposes a constrained canonical polyadic (CP) tensor decomposition method with low-rank factor matrices. In this way, we allow the CP decomposition with high rank while keeping the number of the model parameters small. First, we propose an algorithm to decompose the tensors into factor matrices of given ranks. Second, we propose an algorithm which can determine the ranks of the factor matrices automatically, such that the fitting error is bounded by a user- selected constant. The algorithms are verified on the decomposition of a tensor of the MNIST hand-written image dataset.

BibTeX

@inproceedings{icassp2021_canonicalpolyadi,
  title = {Canonical Polyadic Tensor Decomposition With Low-Rank Factor Matrices},
  author = {Anh-Huy Phan and Petr Tichavský and Konstantin Sobolev and Konstantin Sozykin and Dmitry Ermilov and Andrzej Cichocki},
  booktitle = {ICASSP 2021},
  year = {2021}
}