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An efficient matrix bi-factorization alternative optimization method for low-rank matrix recovery and completion.

Yuanyuan Liu1, L C Jiao, Fanhua Shang

  • 1Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi'an 710071, China.

Neural Networks : the Official Journal of the International Neural Network Society
|July 30, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient Matrix Bi-Factorization (MBF) method to reduce the computational cost of matrix rank minimization problems. MBF approximates trace norm minimization, offering a faster alternative to iterative singular value decomposition (SVD) methods.

Keywords:
Low rank representationLow-rank and sparse matrix decompositionMatrix completionRank minimizationTrace norm minimization

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Area of Science:

  • Machine Learning
  • Data Mining
  • Computer Vision

Background:

  • Matrix rank minimization problems are central to machine learning, data mining, and computer vision.
  • Current methods rely on convex relaxations using trace norm minimization, requiring iterative singular value decomposition (SVD).
  • These iterative SVD computations lead to high computational costs.

Purpose of the Study:

  • To propose an efficient Matrix Bi-Factorization (MBF) method.
  • To approximate trace norm minimization problems and reduce the computational burden of SVD.
  • To address various low-rank matrix recovery and completion tasks.

Main Methods:

  • Developed an efficient Matrix Bi-Factorization (MBF) method.
  • Formulated three small-scale matrix trace norm models for low-rank and sparse matrix decomposition (LRSD), low-rank representation (LRR), and low-rank matrix completion (MC).
  • Designed two linearized proximal alternative optimization algorithms to solve these models.

Main Results:

  • The MBF method effectively approximates trace norm minimization problems.
  • The proposed algorithms efficiently solve LRSD, LRR, and MC problems.
  • Experimental results demonstrate the efficiency, robustness, and effectiveness of MBF compared to existing methods.

Conclusions:

  • The Matrix Bi-Factorization (MBF) method offers a computationally efficient approach for matrix rank minimization.
  • MBF is applicable to a broad range of low-rank matrix recovery and completion problems.
  • The proposed optimization algorithms provide effective solutions for LRSD, LRR, and MC.