A Probabilistic Approach to Robust Matrix Factorization

Naiyan Wang¹, Tiansheng Yao², Jingdong Wang³, and Dit-Yan Yeung¹

¹Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China
winsty@gmail.com
dyyeung@cse.ust.hk

²Computer Science Department, University of California, Los Angeles, USA
tsyao@cs.ucla.edu

³Microsoft Research Asia, No. 5 Danling Street, Haidian District, Beijing 100080, China
jingdw@microsoft.com

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 ₁ loss and an ₂ 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.

LNCS 7578, p. 126 ff.

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