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Low-Rank Matrix Recovery via Continuation-Based Approximate Low-Rank Minimization

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PRICAI 2018: Trends in Artificial Intelligence (PRICAI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11012))

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Abstract

Low-rank matrix recovery (LRMR) is to recover the underlying low-rank structure from the degraded observations, and has myriad formulations, for example robust principal component analysis (RPCA). As a core component of LRMR, the low-rank approximation model attempts to capture the low-rank structure by approximating the \(\ell _0\)-norm of all the singular values of a low-rank matrix, i.e., the number of the non-zero singular values. Towards this purpose, this paper develops a low-rank approximation model by jointly combining a parameterized hyperbolic tangent (tanh) function with the continuation process. Specificially, the continuation process is exploited to impose the parameterized tanh function to approximate the \(\ell _0\)-norm. We then apply the proposed low-rank model to RPCA and refer to it as tanh-RPCA. Convergence analysis on optimization, and experiments of background subtraction on seven challenging real-world videos show the efficacy of the proposed low-rank model through comparing tanh-RPCA with several state-of-the-art methods.

X. Zhang and Y. Gao—Contributed equally to this work and this work was supported by the National Key Research and Development Program of China [2016YFB0200401], the National Natural Science Foundation of China [U1435222] and the National High-tech R&D Program [2015AA020108].

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Notes

  1. 1.

    F-measure is the harmonic average of the precision and recall, with the best value at 1 (perfect precision and recall) and the worst at 0.

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Authors and Affiliations

  1. State Key Laboratory of High Performance Computing, NUDT, Changsha, China

    Xiang Zhang, Long Lan & Xiaowei Guo

  2. Science and Technology on Parallel and Distributed Laboratory, NUDT, Changsha, China

    Yongqiang Gao & Zhigang Luo

  3. Department of Computer Science and Technology, College of Computer, NUDT, Changsha, China

    Xuhui Huang

  4. College of Computer, NUDT, Changsha, 410073, China

    Xiang Zhang, Yongqiang Gao, Long Lan, Xiaowei Guo, Xuhui Huang & Zhigang Luo

Authors
  1. Xiang Zhang
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  2. Yongqiang Gao
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  3. Long Lan
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  4. Xiaowei Guo
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  5. Xuhui Huang
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  6. Zhigang Luo
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Corresponding authors

Correspondence to Yongqiang Gao or Zhigang Luo .

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Editors and Affiliations

  1. Southeast University, Nanjing, China

    Xin Geng

  2. University of Tasmania, Hobart, Tasmania, Australia

    Byeong-Ho Kang

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Zhang, X., Gao, Y., Lan, L., Guo, X., Huang, X., Luo, Z. (2018). Low-Rank Matrix Recovery via Continuation-Based Approximate Low-Rank Minimization. In: Geng, X., Kang, BH. (eds) PRICAI 2018: Trends in Artificial Intelligence. PRICAI 2018. Lecture Notes in Computer Science(), vol 11012. Springer, Cham. https://doi.org/10.1007/978-3-319-97304-3_43

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  • DOI: https://doi.org/10.1007/978-3-319-97304-3_43

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