Tensor completion via group-sparse regularization

Bo Yang, Gang Wang, Nikolaos Sidiropoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

To enable low-rank tensor completion and factorization, this paper puts forth a novel tensor rank regularization method based on the ℓ1,2-norm of the tensor's parallel factor analysis (PARAFAC) factors. Specifically, for an N-way tensor, upon collecting the magnitudes of its rank-1 components in a vector, the proposed regularizer controls the tensor's rank by inducing sparsity in the vector of magnitudes through ℓ1/N (pseudo)-norm regularization. Our approach favors sparser magnitude vectors than existing ℓ2/N- and ℓ1-based alternatives. With an eye towards large-scale tensor mining applications, we also develop efficient and highly scalable solvers for tensor factorization and completion using the proposed criterion. Extensive numerical tests using both synthetic and real data demonstrate that the proposed criterion is better in terms of revealing the correct number of components and estimating the underlying factors than competing alternatives.

Original languageEnglish (US)
Title of host publicationConference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1750-1754
Number of pages5
ISBN (Electronic)9781538639542
DOIs
StatePublished - Mar 1 2017
Event50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, United States
Duration: Nov 6 2016Nov 9 2016

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393

Other

Other50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
CountryUnited States
CityPacific Grove
Period11/6/1611/9/16

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