Robust bilinear factorization with missing and grossly corrupted observations

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

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint/mixed relaxations (i.e., l1-norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods.

Original languageEnglish (US)
Pages (from-to)53-72
Number of pages20
JournalInformation Sciences
Volume307
DOIs
StatePublished - Jun 20 2015

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Factorization
Pursuit
Principal Components
Matrix Completion
Low-rank Matrices
Sparse matrix
Trace
Matrix Completion Problem
Method of multipliers
Norm
Alternating Direction Method
Analysis of Algorithms
Factorization Method
L1-norm
Large-scale Problems
Convergence Analysis
Computer Vision
Updating
Signal Processing
Image Processing

Keywords

  • Compressive principal component pursuit
  • Low-rank matrix recovery and completion
  • Robust matrix completion
  • Robust principal component analysis

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management

Cite this

Robust bilinear factorization with missing and grossly corrupted observations. / Shang, Fanhua; Liu, Yuanyuan; Tong, Hanghang; Cheng, James; Cheng, Hong.

In: Information Sciences, Vol. 307, 20.06.2015, p. 53-72.

Research output: Contribution to journalArticle

Shang, Fanhua ; Liu, Yuanyuan ; Tong, Hanghang ; Cheng, James ; Cheng, Hong. / Robust bilinear factorization with missing and grossly corrupted observations. In: Information Sciences. 2015 ; Vol. 307. pp. 53-72.
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