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Adaptive algorithms for low-rank and sparse matrix recovery with truncated nuclear norm

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Abstract

Recent studies have shown that the use of the truncated nuclear norm (TNN) in low-rank and sparse matrix decomposition (LRSD) can realize a better approximation to rank function of matrix, and achieve effectively recovery effects. This paper addresses the algorithms for LRSD with adaptive TNN (LRSD-ATNN), and designs an efficient algorithmic frame inspired by the alternating direction method of multiple (ADMM) and the accelerated proximal gradient approach (APG). To establish the adaptive algorithms, the method of singular value estimate is utilized to find adaptively the number of truncated singular value. Experimental results on synthetic data as well as real visual data show the superiority of the proposed algorithm in effectiveness in comparison with the state-of-the-art methods.

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Notes

  1. http://perception.i2r.astar.edu.sg/bk_model/bk_index.html.

  2. http://perception.i2r.astar.edu.sg/bk_model/bk_index.html.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China under Grant 61672477.

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  1. Department of Applied Mathematics, College of Sciences, China Jiliang University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Wenchao Qian & Feilong Cao

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  1. Wenchao Qian
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Correspondence to Feilong Cao.

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Qian, W., Cao, F. Adaptive algorithms for low-rank and sparse matrix recovery with truncated nuclear norm. Int. J. Mach. Learn. & Cyber. 10, 1341–1355 (2019). https://doi.org/10.1007/s13042-018-0814-9

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