A Cyclic Weighted Median Method for L1 Low-Rank Matrix Factorization with Missing Entries

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Authors Deyu Meng, Zongben Xu, Lei Zhang and Ji Zhao
Journal/Conference Name AAAI Conference on Artificial Intelligence (AAAI-13)
Paper Category
Paper Abstract A challenging problem in machine learning, information retrieval and computer vision research is how to recover a low-rank representation of the given data in the presence of outliers and missing entries. The L1-norm low-rank matrix factorization (LRMF) has been a popular approach to solving this problem. However, L1-norm LRMF is difficult to achieve due to its non-convexity and non-smoothness, and existing methods are often in-efficient and fail to converge to a desired solution. In this paper we propose a novel cyclic weighted median (CWM) method, which is intrinsically a coordinate decent algorithm, for L1-norm LRMF. The CWM method minimizes the objective by solving a sequence of scalar minimization sub-problems, each of which is convex and can be easily solved by the weighted median filter. The extensive experimental results validate that the CWM method outperforms state-of-the-arts in terms of both accuracy and computational efficiency.
Date of publication 2013
Code Programming Language MATLAB
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