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Sparse subspace clustering with low-rank transformation

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Abstract

In order to solve the problem that sparse subspace clustering cannot effectively cluster the dataset under non-independent assumption, this paper proposes the sparse subspace clustering with low-rank transformation, which merges the low-rank transformation into sparse subspace clustering. The low-rank transformation can not only reduce variations within the subspaces, but also increase separations between the subspaces. This guarantees that property of these datasets is altered from inconsistent independent assumption to asymptotic consistent independent assumption, ultimately to consistent independent assumption. Sparse subspace clustering with low-rank transformation is formulated as the minimization optimizations with two variables, which can be solved by an iterative strategy including the clustering and computing the optimal transformation. Experimental results on the synthetic datasets show that sparse subspace clustering with low-rank transformation is robust to synthetic dataset with noise and its classification error is approximately 75% lower than that of sparse subspace clustering. Experimental results on face clustering on the Yale Extend B dataset and motion segmentation on Hopkins 155 dataset show that the proposed approach significantly outperforms sparse subspace clustering.

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Acknowledgements

This work was supported by Public Welfare Industry (Agriculture) Research Projects Level-2 (201503116-04-06), National Science and Technology Support Program (2014BAD12B01-1-3), Open Fund of Key Laboratory for Efficient Utilization of Agricultural Water Resources in the Ministry of Agriculture (2015004) and Postdoctoral Foundation of Heilongjiang Province (LBH-Z15020).

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Authors and Affiliations

  1. College of Engineering, Northeast Agricultural University, Harbin, China

    Gang Xu

  2. College of Economics and Management, Northeast Agricultural University, Harbin, China

    Mei Yang

  3. College of Science, Northeast Agricultural University, Harbin, China

    Qiufeng Wu

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  1. Gang Xu
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  2. Mei Yang
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  3. Qiufeng Wu
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Correspondence to Qiufeng Wu.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work and there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

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Xu, G., Yang, M. & Wu, Q. Sparse subspace clustering with low-rank transformation. Neural Comput & Applic 31, 3141–3154 (2019). https://doi.org/10.1007/s00521-017-3259-2

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