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Rank–sparsity balanced representation for subspace clustering

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Abstract

Subspace learning has many applications such as motion segmentation and image recognition. The existing algorithms based on self-expressiveness of samples for subspace learning may suffer from the unsuitable balance between the rank and sparsity of the expressive matrix. In this paper, a new model is proposed that can balance the rank and sparsity well. This model adopts the log-determinant function to control the rank of solution. Meanwhile, the diagonals are penalized, rather than the strict zero-restriction on diagonals. This strategy makes the rank–sparsity balance more tunable. We furthermore give a new graph construction from the low-rank and sparse solution, which absorbs the advantages of the graph constructions in the sparse subspace clustering and the low-rank representation for further clustering. Numerical experiments show that the new method, named as RSBR, can significantly increase the accuracy of subspace clustering on the real-world data sets that we tested.

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Notes

  1. We say \(\mathbf{C}_k\) is connected if a undirected graph having the adjoint matrix \(|\mathbf{C}_k|+|\mathbf{C}_k^T|\) is connected.

  2. http://vision.jhu.edu/code/fetchcode.php?id=4.

  3. http://www.vision.jhu.edu/data/hopkins155.

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

  5. http://www.escience.cn/people/fpnie/papers.html.

  6. In this case, \(\mathbf{C}\) should be a block-diagonal matrix of K connected blocks under a permutation.

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Acknowledgements

The work was supported in part by NSFC Projects 11571312 and 91730303, and National Basic Research Program of China (973 Program) 2015CB352503.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, China

    Yuqing Xia

  2. Department of Mathematics and the State Key Laboratory of CAD&CG, Zhejiang University, Yuquan Campus, Hangzhou, 310027, China

    Zhenyue Zhang

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  1. Yuqing Xia
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Correspondence to Zhenyue Zhang.

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Xia, Y., Zhang, Z. Rank–sparsity balanced representation for subspace clustering. Machine Vision and Applications 29, 979–990 (2018). https://doi.org/10.1007/s00138-018-0918-y

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