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Robust Subspace Segmentation by Self-Representation Constrained Low-Rank Representation

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Abstract

Low-rank representation (LRR) and its variants have been proved to be powerful tools for handling subspace segmentation problems. In this paper, we propose a new LRR-related algorithm, termed self-representation constrained low-rank presentation (SRLRR). SRLRR contains a self-representation constraint which is used to compel the obtained coefficient matrices can be reconstructed by themselves. An optimization algorithm for solving SRLRR problem is also proposed. Moreover, we present an alternative formulation of SRLRR so that SRLRR can be regarded as a kind of Laplacian regularized LRR. Consequently, the relationships and comparisons between SRLRR and some existing Laplacian regularized LRR-related algorithms have been discussed. Finally, subspace segmentation experiments conducted on both synthetic and real databases show that SRLRR dominates the related algorithms.

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Notes

  1. According to the descriptions in [30], this constraint can make \({\mathbf {Z}}\) be more powerful to reveal the intrinsic structures of data sets.

  2. Namely, \({\mathbf {L}}={\mathbf {D}}-{\mathbf {W}}\), where \({\mathbf {W}}\) is an affinity matrix constructed by using KNN, \({\mathbf {D}}\) is a diagonal matrix with \({\mathbf {D}}_{ii}=\sum _{j}{\mathbf {W}}_{ij}\).

  3. \({\mathbf {Z}}\) is a locally reconstruction coefficient matrix.

  4. The Matlab code of NSLLRR can be found on http://www.cis.pku.edu.cn/faculty/vision/zlin/sparse_graph_LRR.m. Because NSLLRR is the extension of GLRR and SMR, we do not use GLRR and SMR for comparisons.

  5. The segmentation accuracy is defined as the ratio between number of correct classified points to total number of points.

  6. It also contains a sequence of 5 motions which is called “dancing”. We neglect this sub-database in our experiments.

  7. The choices of PCA dimension is followed the suggestion in [3].

  8. Segmentation error = 1 − segmentation accuracy.

  9. It can be seen that the curves plotted in Fig. 8b and most curves in Fig. 8a, c are consistent with the interpretation.

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Authors and Affiliations

  1. Department of Computer Science, Shanghai Maritime University, Haigang Avenue 1550, Shanghai, China

    Lai Wei, Xiaofeng Wang, Aihua Wu, Rigui Zhou & Changming Zhu

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  1. Lai Wei
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  2. Xiaofeng Wang
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Correspondence to Lai Wei.

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The authors declared that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, 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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Wei, L., Wang, X., Wu, A. et al. Robust Subspace Segmentation by Self-Representation Constrained Low-Rank Representation. Neural Process Lett 48, 1671–1691 (2018). https://doi.org/10.1007/s11063-018-9783-y

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