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Accelerated matrix recovery via random projection based on inexact augmented Lagrange multiplier method

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Abstract

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

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Authors and Affiliations

  1. School of Sciences, Tianjin University, Tianjin, 300072, China

    Ping Wang  (王 萍), Chuhan Zhang  (张楚涵), Sijia Cai  (蔡思佳) & Linhao Li  (李林昊)

Authors
  1. Ping Wang  (王 萍)
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  2. Chuhan Zhang  (张楚涵)
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  3. Sijia Cai  (蔡思佳)
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  4. Linhao Li  (李林昊)
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Corresponding author

Correspondence to Sijia Cai  (蔡思佳).

Additional information

Supported by National Natural Science Foundation of China (No.51275348) and College Students Innovation and Entrepreneurship Training Program of Tianjin University (No.201210056339).

Wang Ping, born in 1967, female, Dr, Prof.

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Wang, P., Zhang, C., Cai, S. et al. Accelerated matrix recovery via random projection based on inexact augmented Lagrange multiplier method. Trans. Tianjin Univ. 19, 293–299 (2013). https://doi.org/10.1007/s12209-013-2135-0

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  • DOI: https://doi.org/10.1007/s12209-013-2135-0

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