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Low Rank Representation on Grassmann Manifolds

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Computer Vision – ACCV 2014 (ACCV 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9003))

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Abstract

Low-rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space into the LRR model on Grassmann manifold. The new method has many applications in computer vision tasks. The paper conducts the experiments over two real world examples, clustering handwritten digits and clustering dynamic textures. The experiments show the proposed method outperforms a number of existing methods.

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Notes

  1. 1.

    As the manifold is generally no longer linear, so the linear combination on the manifold should be implemented via exp and log operations on the manifold. We ignore this for the simplicity of presenting our idea.

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Acknowledgements

The research project is supported by the Australian Research Council (ARC) through the grant DP130100364 and also partially supported by National Natural Science Foundation of China under Grant No.61390510, 61133003, 61370119, 61171169, 61227004 and Beijing Natural Science Foundation No.4132013.

Author information

Authors and Affiliations

  1. Beijing Key Laboratory of Multimedia and Intelligent Software Technology, College of Metropolitan Transportation, Beijing University of Technology, Beijing, China

    Boyue Wang, Yongli Hu, Yanfeng Sun & Baocai Yin

  2. School of Computing and Mathematics, Charles Sturt University, Bathurst, NSW, 2795, Australia

    Junbin Gao

Authors
  1. Boyue Wang
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  2. Yongli Hu
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  3. Junbin Gao
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  4. Yanfeng Sun
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  5. Baocai Yin
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Corresponding author

Correspondence to Junbin Gao .

Editor information

Editors and Affiliations

  1. Technische Universität München, Garching, Bayern, Germany

    Daniel Cremers

  2. University of Adelaide, Adelaide, South Australia, Australia

    Ian Reid

  3. Keio University, Yokohama, Kanagawa, Japan

    Hideo Saito

  4. University of California at Merced, Merced, California, USA

    Ming-Hsuan Yang

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Wang, B., Hu, Y., Gao, J., Sun, Y., Yin, B. (2015). Low Rank Representation on Grassmann Manifolds. In: Cremers, D., Reid, I., Saito, H., Yang, MH. (eds) Computer Vision – ACCV 2014. ACCV 2014. Lecture Notes in Computer Science(), vol 9003. Springer, Cham. https://doi.org/10.1007/978-3-319-16865-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-16865-4_6

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  • Online ISBN: 978-3-319-16865-4

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