Subspace Segmentation by Low Rank Representation via the Sparse-Prompting Quasi-Rank Function

作     者：Li, Haiyang Wang, Yusi Zhang, Qian Xing, Zhiwei Lin, Shoujin Peng, Jigen 

作者机构：Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 611731 Peoples R China Xian Polytech Univ Sch Sci Xian 710048 Peoples R China Zhongshan MLTOR CNC Technol Co Ltd Zhongshan 528400 Peoples R China 

出 版 物：《IEEE ACCESS》 (IEEE Access)

年 卷 期：2022年第10卷

页      面：55753-55765页

核心收录：

基　　金：National Science Foundation of China [12031003, 11771347] Basic Research Joint Funding Project of University and Guangzhou City 

主　　题：Sparse matrices Minimization Databases Clustering algorithms Gaussian noise Signal processing algorithms Optimization Band restricted thresholding operator face clustering low rank representation motion segmentation sparse-prompting quasi-rank function subspace segmentation 

摘      要：In this paper, a general optimization formulation is proposed for the subspace segmentation by low rank representation via the sparse-prompting quasi-rank function. We prove that, with the clean data from independent linear subspaces, the optimal solution to our optimization formulation not only is the lowest rank but also forms a block-diagonal matrix, which implies that it is reasonable to use any sparse-prompting quasi-rank function as the measure of the low rank in subspace clustering. With the data contaminated by Gaussian noise and/or gross errors, the alternating direction method of multipliers is applied to solving it and every sub-optimization problem has a closed-form optimal solution when the band restricted thresholding operator induced by its corresponding sparse-prompting function has an analytic expression, in which the gross errors part is replaced with the sparse-prompting matrix function. Finally, taking a specific sparse-prompting function, the fraction function, we conduct a series of simulations on different databases to get the performance of our algorithm tested, and experimental results show that our algorithm can obtain lower clustering error rate and higher value of evaluation indicators ACC, NMI and ARI than other state-of-the-art subspace clustering algorithms on different databases.