Canonical polyadic tensor decomposition with low-rank factor matrices

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

Research output: Contribution to journalConference articlepeer-review

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.

Original languageEnglish
Pages (from-to)4690-4694
Number of pages5
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2021-June
DOIs
Publication statusPublished - 2021
Event2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021 - Virtual, Toronto, Canada
Duration: 6 Jun 202111 Jun 2021

Keywords

  • CANDECOMP
  • Low-rank constraint
  • PARAFAC
  • Rank minimization
  • Tensor decomposition

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