Rank-one tensor injection: A novel method for canonical polyadic tensor decomposition

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Canonical polyadic decomposition of tensor is to approximate or express the tensor by sum of rank-1 tensors. When all or almost all components of factor matrices of the tensor are highly collinear, the decomposition becomes difficult. Algorithms, e.g., the alternating algorithms, require plenty of iterations, and may get stuck in false local minima. This paper proposes a novel method for such decompositions. The method injects one or a few rank-1 tensors into the data tensor in order to control the decompositions of the rank-expanded data, while still preserving the estimation accuracy of the original tensor. To achieve this, we develop a method to automatically generate the injected tensor which satisfies a specific estimation accuracy such that this tensor should not dominate rank-1 tensors of the data tensor, but is still able to be retrieved with a sufficient accuracy. Simulations on tensors with highly collinear factor matrices will illustrate efficiency of the proposed injecting method.

Original languageEnglish
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2549-2553
Number of pages5
ISBN (Electronic)9781479999880
DOIs
Publication statusPublished - 18 May 2016
Externally publishedYes
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: 20 Mar 201625 Mar 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/TerritoryChina
CityShanghai
Period20/03/1625/03/16

Keywords

  • CANDECOMP/PARAFAC
  • Cramer-Rao-induced bound
  • tensor decomposition
  • tensor deflation
  • tensor injection

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