A further improvement of a fast damped Gauss-Newton algorithm for candecomp-parafac tensor decomposition

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16 Citations (Scopus)

Abstract

In this paper, a novel implementation of the damped Gauss-Newton algorithm (also known as Levenberg-Marquart) for the CANDECOMP-PARAFAC (CP) tensor decomposition is proposed. The method is based on a fast inversion of the approximate Hessian for the problem. It is shown that the inversion can be computed on O(NR6) operations, where N and R is the tensor order and rank, respectively. It is less than in the best existing state-of-the art algorithm with O(N3R6) operations. The damped Gauss-Newton algorithm is suitable namely for difficult scenarios, where nearly-colinear factors appear in several modes simultaneously. Performance of the method is shown on decomposition of large tensors (100 × 100 × 100 and 100 × 100 × 100 × 100) of rank 5 to 90.

Original languageEnglish
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages5964-5968
Number of pages5
DOIs
Publication statusPublished - 18 Oct 2013
Externally publishedYes
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: 26 May 201331 May 2013

Publication series

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

Conference

Conference2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
Country/TerritoryCanada
CityVancouver, BC
Period26/05/1331/05/13

Keywords

  • canonical polyadic decomposition
  • damped Gauss-Newton algorithm
  • Multilinear models

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