Factor matrix trace norm minimization for low-rank tensor completion

Yuanyuan Liu, Fanhua Shang, Hong Cheng, James Cheng, Hanghang Tong

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

12 Scopus citations

Abstract

Most existing low-n-rank minimization algorithms for tensor completion suffer from high computational cost due to involving multiple singular value decompositions (SVDs) at each iteration. To address this issue, we propose a novel factor matrix trace norm minimization method for tensor completion problems. Based on the CANDECOMP/PARAFAC (CP) decomposition, we first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode-n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, which leads to a convex combination problem of much smaller scale matrix nuclear norm minimization. Finally, we develop an efficient alternating direction method of multipliers (ADMM) scheme to solve the proposed problem. Experimental results on both synthetic and real-world data validate the effectiveness of our approach. Moreover, our method is significantly faster than the state-of-the-art approaches and scales well to handle large datasets.

Original languageEnglish (US)
Title of host publicationSIAM International Conference on Data Mining 2014, SDM 2014
EditorsPang Ning-Tan, Srinivasan Parthasarathy, Zoran Obradovic, Mohammed Zaki, Arindam Banerjee, Chandrika Kamath
PublisherSociety for Industrial and Applied Mathematics Publications
Pages866-874
Number of pages9
ISBN (Electronic)9781510811515
DOIs
StatePublished - Jan 1 2014
Event14th SIAM International Conference on Data Mining, SDM 2014 - Philadelphia, United States
Duration: Apr 24 2014Apr 26 2014

Publication series

NameSIAM International Conference on Data Mining 2014, SDM 2014
Volume2

Other

Other14th SIAM International Conference on Data Mining, SDM 2014
CountryUnited States
CityPhiladelphia
Period4/24/144/26/14

ASJC Scopus subject areas

  • Computer Science Applications
  • Software

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  • Cite this

    Liu, Y., Shang, F., Cheng, H., Cheng, J., & Tong, H. (2014). Factor matrix trace norm minimization for low-rank tensor completion. In P. Ning-Tan, S. Parthasarathy, Z. Obradovic, M. Zaki, A. Banerjee, & C. Kamath (Eds.), SIAM International Conference on Data Mining 2014, SDM 2014 (pp. 866-874). (SIAM International Conference on Data Mining 2014, SDM 2014; Vol. 2). Society for Industrial and Applied Mathematics Publications. https://doi.org/10.1137/1.9781611973440.99