Canonical polyadic decomposition: From 3-way to N-way

Guoxu Zhou, Zhaoshui He, Yu Zhang, Qibin Zhao, Andrzej Cichocki

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

5 Citations (Scopus)

Abstract

Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions are widely applied to analyze high order data, i.e. N-way tensors. Existing CP decomposition methods use alternating least square (ALS) iterations and hence need to compute the inverse of matrices and unfold tensors frequently, which are very time consuming for large-scale data and when N is large. Fortunately, once at least one factor has been correctly estimated, all the remaining factors can be computed efficiently and uniquely by using a series of rank-one approximations. Motivated by this fact, to perform a full N-way CP decomposition, we run 3-way CP decompositions on a sub-tensor to estimate two factors first. Then the remaining factors are estimated via an efficient Khatri-Rao product recovering procedure. In this way the whole ALS iterations with respect to each mode are avoided and the efficiency can be significantly improved. Simulations show that, compared with ALS based CP decomposition methods, the proposed method is more efficient and is easier to escape from local solutions for high order tensors.

Original languageEnglish
Title of host publicationProceedings of the 2012 8th International Conference on Computational Intelligence and Security, CIS 2012
Pages391-395
Number of pages5
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event2012 8th International Conference on Computational Intelligence and Security, CIS 2012 - Guangzhou, Guangdong, China
Duration: 17 Nov 201218 Nov 2012

Publication series

NameProceedings of the 2012 8th International Conference on Computational Intelligence and Security, CIS 2012

Conference

Conference2012 8th International Conference on Computational Intelligence and Security, CIS 2012
Country/TerritoryChina
CityGuangzhou, Guangdong
Period17/11/1218/11/12

Keywords

  • alternating least square
  • CP (PARAFAC) decompositions
  • Khatri-Rao product
  • tensor decompositions

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