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Robust subspace clustering via joint weighted Schatten-p norm and Lq norm minimization

[+] Author Affiliations
Tao Zhang, Zhenmin Tang, Qing Liu

Nanjing University of Science and Technology, School of Computer Science and Engineering, Nanjing, China

J. Electron. Imaging. 26(3), 033021 (Jun 06, 2017). doi:10.1117/1.JEI.26.3.033021
History: Received January 23, 2017; Accepted May 15, 2017
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Abstract.  Low-rank representation (LRR) has been successfully applied to subspace clustering. However, the nuclear norm in the standard LRR is not optimal for approximating the rank function in many real-world applications. Meanwhile, the L21 norm in LRR also fails to characterize various noises properly. To address the above issues, we propose an improved LRR method, which achieves low rank property via the new formulation with weighted Schatten-p norm and Lq norm (WSPQ). Specifically, the nuclear norm is generalized to be the Schatten-p norm and different weights are assigned to the singular values, and thus it can approximate the rank function more accurately. In addition, Lq norm is further incorporated into WSPQ to model different noises and improve the robustness. An efficient algorithm based on the inexact augmented Lagrange multiplier method is designed for the formulated problem. Extensive experiments on face clustering and motion segmentation clearly demonstrate the superiority of the proposed WSPQ over several state-of-the-art methods.

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Citation

Tao Zhang ; Zhenmin Tang and Qing Liu
"Robust subspace clustering via joint weighted Schatten-p norm and Lq norm minimization", J. Electron. Imaging. 26(3), 033021 (Jun 06, 2017). ; http://dx.doi.org/10.1117/1.JEI.26.3.033021


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