Low Rank Subspace Clustering Algorithm

Subspace clustering has a lot of applications in face recognition,image segmentation and image clustering.Meanwhile,Low rank representation is widely used in subspace clustering.However,minimizing the rank of the data matrix is an NP hard problem.Instead of solving such an NP hard problem,the researchers usually use the trace norm as the convex relaxation of the rank function.Therefore,finding a better norm to make the subspace matrix have a more accurate low rank structure becomes a challenging problem.With the richness of data types and feature extraction methods,multi-view data becomes more and more obtainable.How to improve clustering results by using the diversity and complementarity of multi-view data is the key issue of multi-view clustering.This article focuses on the subspace clustering algorithm on single-view and multi-view data,and studies how to effectively use low-rank constraint and multi-view data to enhance the clustering effect.This article includes the following three aspects of research:(1)Joint Schatten-p norm and p norm Multiview Subspace ClusteringIn order to obtain a subspace representation matrix with a better low-rank structure,this paper used the Schatten p norm to approximate the rank.It was proved that,when p approaches 0,the schatten p norm is a closer approximation to the rank than the nuclear norm.Therefore,the schatten p norm is used instead of the nuclear norm.In order to enhance the robustness of the proposed algorithm,the_pnorm is used to the error term.The experimental results show that the Sp-SC algorithm achieves the best results on three data sets and can also achieve good results in the noise-free data of Extended Yale B.This shows that the Sp-SC algorithm has great robustness.(2)Nuclear Norm Constrained Multiview Subspace ClusteringIn order to effectively use the diversity and complementarity of multi-view data,this paper used the same cluster indicator matrix in different views and alternately learn cluster indication matrix in different views.In order to make the subspace representation matrix have a low rank structure,the nuclear norm constraints are used in the subspace representation matrices.Finally,this paper solved the algorithm by Augmented Lagrangian method and alternating direction method and the experiments demonstrates the good performance of our algorithm.(3)Schatten p norm Constrained Multiview Subspace ClusteringThis paper generalizes the schatten norm from the single view algorithm to multi-view algorithm.Similarly,the same cluster indicator matrix is used in different views.It can be analyzed that when p=1,the Sp-MVSC algorithm and the LR-MVSC algorithm are equivalent,and it can be said that LR-MVSC is a special case of Sp-MVSC.Experimental results show that when p is closer to 0,the algorithm works better.Sp-MVSC algorithm(p=0.1)achieved the best results on all three data sets...