Overcomplete tensor decomposition via convex optimization

Qiuwei Li, Ashley Prater, Lixin Shen, Gongguo Tang

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

8 Scopus citations

Abstract

This work develops theories and computational methods for overcomplete, non-orthogonal tensor decomposition using convex optimization. Under an incoherence condition of the rank-one factors, we show that one can retrieve tensor decomposition by solving a convex, infinite-dimensional analog of ℓ1 minimization on the space of measures. The optimal value of this optimization defines the tensor nuclear norm. Two computational schemes are proposed to solve the infinite-dimensional optimization: semidefinite programs based on sum-of-squares relaxations and nonlinear programs that are an exact reformulation of the tensor nuclear norm. The latter exhibits superior performance compared with the state-of-the-art tensor decomposition methods.

Original languageEnglish (US)
Title of host publication2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages53-56
Number of pages4
ISBN (Print)9781479919635
DOIs
StatePublished - Jan 14 2016
Event6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 - Cancun, Mexico
Duration: Dec 13 2015Dec 16 2015

Other

Other6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
CountryMexico
CityCancun
Period12/13/1512/16/15

ASJC Scopus subject areas

  • Signal Processing
  • Computational Mathematics

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    Li, Q., Prater, A., Shen, L., & Tang, G. (2016). Overcomplete tensor decomposition via convex optimization. In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 (pp. 53-56). [7383734] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CAMSAP.2015.7383734