Low-rank matrix decomposition in L1-norm by dynamic systems |
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Authors: | Yiguang Liu Bingbing Liu Yifei Pu Xiaohui Chen Hong Cheng |
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Affiliation: | 1. Vision and Image Processing Lab, College of Computer, Sichuan University, Chengdu 610065, PR China;2. College of Computer and Information Technology China Three Gorges University Yichang, 443002, PR China;3. Pattern Recognition and Machine Intelligence Lab., University of Electronic Science and Technology of China, Chengdu 611731, PR China;4. Institute for Infocomm Research, A*STAR, 1 Fusionopolis Way, Singapore 138632 |
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Abstract: | Low-rank matrix approximation is used in many applications of computer vision, and is frequently implemented by singular value decomposition under L2-norm sense. To resist outliers and handle matrix with missing entries, a few methods have been proposed for low-rank matrix approximation in L1 norm. However, the methods suffer from computational efficiency or optimization capability. Thus, in this paper we propose a solution using dynamic system to perform low-rank approximation under L1-norm sense. From the state vector of the system, two low-rank matrices are distilled, and the product of the two low-rank matrices approximates to the given measurement matrix with missing entries, in L1 norm. With the evolution of the system, the approximation accuracy improves step by step. The system involves a parameter, whose influences on the computational time and the final optimized two low-rank matrices are theoretically studied and experimentally valuated. The efficiency and approximation accuracy of the proposed algorithm are demonstrated by a large number of numerical tests on synthetic data and by two real datasets. Compared with state-of-the-art algorithms, the newly proposed one is competitive. |
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Keywords: | Low-rank matrix approximation Dynamic system L1 norm Computational efficiency |
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