基于TL<sub>1</sub>范数约束的子空间聚类方法

doi:10.11999/JEIT170193

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Abstract The TL₁ norm is applied to propose a new optimization model for the study of subspace clustering. Although the optimization is nonconvex, in the case of non-noise, it proves that the optimal solution of the proposed model is the coefficient matrix with block-diagonal structure, which provides the theoretical guarantee for the latter spectral clustering. In the case of dealing with noise, the constraint condition of this model is presented to be equivalent with the optimal model using the corrected data as the dictionary, which contributes to improving the clustering accuracy. Then, the alternating direction method of Lagrangian multipliers is applied to solving the unknown matrices. Experimental results show that subspace clustering method based on TL₁ norm not only enhances the sparsity of coefficient matrix, but also is superior to low-rank subspace clustering and sparse subspace clustering method in terms of clustering accuracy and robustness to noise.

Key words： TL₁ norm Subspace clustering method Sparse Low-rank Spectral clustering

Received: 03 March 2017 Published: 14 August 2017

PACS:

TP391

Fund:The National Natural Science Foundation of China (11271297), The Natural Science Foundation of Shaanxi Province (2015JM1020)

Corresponding Authors: LI Haiyang E-mail: fplihaiyang@126.com

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LI Haiyang,WANG Hengyuan. Subspace Clustering Method Based on TL₁ Norm Constraints[J]. JEIT, 2017, 39(10): 2428-2436.

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http://jeit.ie.ac.cn/EN/10.11999/JEIT170193 OR http://jeit.ie.ac.cn/EN/Y2017/V39/I10/2428

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