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Rigidly Self-Expressive Sparse Subspace Clustering

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Trends and Applications in Knowledge Discovery and Data Mining (PAKDD 2016)

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Abstract

Sparse subspace clustering is a well-known algorithm, and it is widely used in many research field nowadays, and a lot effort has been contributed to improve it. In this paper, we propose a novel approach to obtain the coefficient matrix. Compared with traditional sparse subspace clustering (SSC) approaches, the key advantage of our approach is that it provides a new perspective of the self-expressive property. We call it rigidly self-expressive (RSE) property. This new formulation captures the rigidly self-expressive property of the data points in the same subspace, and provides a new formulation for sparse subspace clustering. Extensions to traditional SSC could also be cooperating with this new formulation. We present a first-order algorithm to solve the nonconvex optimization, and further prove that it converges to a KKT point of the nonconvex problem under certain standard assumptions. Extensive experiments on the Extended Yale B dataset, the USPS digital images dataset, and the Columbia Object Image Library shows that for images with up to 30 % missing pixels the clustering quality achieved by our approach outperforms the original SSC.

L. Qiao—The work was partially supported by the National Natural Science Foundation of China under Grant No. 61303264 and Grant No. 61202482.

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Notes

  1. 1.

    http://vision.ucsd.edu/~leekc/ExtYaleDatabase/ExtYaleB.html.

  2. 2.

    http://statweb.stanford.edu/~tibs/ElemStatLearn/data.html.

  3. 3.

    http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php.

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Authors and Affiliations

  1. College of Computer, National University of Defense Technology, Changsha, 410073, China

    Linbo Qiao, Bofeng Zhang, Yipin Sun & Jinshu Su

  2. National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha, 410073, China

    Linbo Qiao & Jinshu Su

Authors
  1. Linbo Qiao
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  2. Bofeng Zhang
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  3. Yipin Sun
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  4. Jinshu Su
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Corresponding author

Correspondence to Linbo Qiao .

Editor information

Editors and Affiliations

  1. New Mexico State University , Las Cruces, New Mexico, USA

    Huiping Cao

  2. University of Technology Sydney , Sydney, New South Wales, Australia

    Jinyan Li

  3. Massey University , Auckland, New Zealand

    Ruili Wang

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Qiao, L., Zhang, B., Sun, Y., Su, J. (2016). Rigidly Self-Expressive Sparse Subspace Clustering. In: Cao, H., Li, J., Wang, R. (eds) Trends and Applications in Knowledge Discovery and Data Mining. PAKDD 2016. Lecture Notes in Computer Science(), vol 9794. Springer, Cham. https://doi.org/10.1007/978-3-319-42996-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-42996-0_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42995-3

  • Online ISBN: 978-3-319-42996-0

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