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An inexact splitting method for the subspace segmentation from incomplete and noisy observations

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Abstract

Subspace segmentation is a fundamental issue in computer vision and machine learning, which segments a collection of high-dimensional data points into their respective low-dimensional subspaces. In this paper, we first propose a model for segmenting the data points from incomplete and noisy observations. Then, we develop an inexact splitting method for solving the resulted model. Moreover, we prove the global convergence of the proposed method. Finally, the inexact splitting method is implemented on the clustering problems in synthetic and benchmark data, respectively. Numerical results demonstrate that the proposed method is computationally efficient, robust as well as more accurate compared with the state-of-the-art algorithms.

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Acknowledgements

The authors would like to thank the financial support from the China Scholarship Council.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, China

    Renli Liang & Yanqin Bai

  2. Department of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Hai Xiang Lin

Authors
  1. Renli Liang
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  2. Yanqin Bai
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  3. Hai Xiang Lin
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Corresponding author

Correspondence to Yanqin Bai.

Additional information

This research was supported by a grant from the National Natural Science Foundation of China (No. 11771275).

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Liang, R., Bai, Y. & Lin, H.X. An inexact splitting method for the subspace segmentation from incomplete and noisy observations. J Glob Optim 73, 411–429 (2019). https://doi.org/10.1007/s10898-018-0684-4

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