Accelerated singular value thresholding for matrix completion

Yao Hu, Debing Zhang, Jun Liu, Jieping Ye, Xiaofei He

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

21 Scopus citations

Abstract

Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real world applications, such as recommender system and image in-painting. These problems can be formulated as a general matrix completion problem. The Singular Value Thresholding (SVT) algorithm is a simple and efficient first-order matrix completion method to recover the missing values when the original data matrix is of low rank. SVT has been applied successfully in many applications. However, SVT is computationally expensive when the size of the data matrix is large, which significantly limits its applicability. In this paper, we propose an Accelerated Singular Value Thresholding (ASVT) algorithm which improves the convergence rate from O(1/N) for SVT to O(1/N 2), where N is the number of iterations during optimization. Specifically, the dual problem of the nuclear norm minimization problem is derived and an adaptive line search scheme is introduced to solve this dual problem. Consequently, the optimal solution of the primary problem can be readily obtained from that of the dual problem. We have conducted a series of experiments on a synthetic dataset, a distance matrix dataset and a large movie rating dataset. The experimental results have demonstrated the efficiency and effectiveness of the proposed algorithm.

Original languageEnglish (US)
Title of host publicationKDD'12 - 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Pages298-306
Number of pages9
DOIs
StatePublished - Sep 14 2012
Event18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2012 - Beijing, China
Duration: Aug 12 2012Aug 16 2012

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Other

Other18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2012
CountryChina
CityBeijing
Period8/12/128/16/12

Keywords

  • adaptive line search scheme
  • matrix completion
  • nesterov's method
  • singular value thresholding

ASJC Scopus subject areas

  • Software
  • Information Systems

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