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A Probabilistic Approach to Robust Matrix Factorization

  • Naiyan Wang
  • Tiansheng Yao
  • Jingdong Wang
  • Dit-Yan Yeung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7578)

Abstract

Matrix factorization underlies a large variety of computer vision applications. It is a particularly challenging problem for large-scale applications and when there exist outliers and missing data. In this paper, we propose a novel probabilistic model called Probabilistic Robust Matrix Factorization (PRMF) to solve this problem. In particular, PRMF is formulated with a Laplace error and a Gaussian prior which correspond to an ℓ1 loss and an ℓ2 regularizer, respectively. For model learning, we devise a parallelizable expectation-maximization (EM) algorithm which can potentially be applied to large-scale applications. We also propose an online extension of the algorithm for sequential data to offer further scalability. Experiments conducted on both synthetic data and some practical computer vision applications show that PRMF is comparable to other state-of-the-art robust matrix factorization methods in terms of accuracy and outperforms them particularly for large data matrices.

Keywords

Online Algorithm Laplace Distribution Structure From Motion Nuclear Norm Computer Vision Application 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Naiyan Wang
    • 1
  • Tiansheng Yao
    • 2
  • Jingdong Wang
    • 3
  • Dit-Yan Yeung
    • 1
  1. 1.Department of Computer Science and EngineeringHong Kong University of Science and TechnologyHong Kong, China
  2. 2.Computer Science DepartmentUniversity of CaliforniaLos AngelesUSA
  3. 3.Microsoft Research AsiaBeijingChina

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