Robust Low-rank Representation And Multi-view Clustering

With the rapid development of electronic information technology,the data descriptions that people have obtained have evolved from single-view descriptions to ubiquitous multi-view descriptions.Compared with the traditional single-view data,multi-view data has better expressive ability for learning tasks,and the complementary information hidden between different view descriptions can effectively improve the stability and generalization ability of learning tasks.Therefore,multi-view data is of great significance to improve the perfor-mance of the target task.In the field of multi-view learning,multi-view clustering is an im-portant research content.In recent years,multi-view clustering algorithms based on tensor Singular Value Decomposition(t-SVD)have become hot research topics because they can effectively mine the complementary information and higher-order information hidden be-tween multiple views.However,existing multi-view clustering algorithms based on t-SVD ignore the significant information between singular values,resulting in a self-expression co-efficient matrix that cannot accurately describe the category structure of the data,making the algorithm unstable.Aiming at this problem,this paper starts from low-rank description and studies robust multi-view subspace clustering algorithms.The specific content is as follows:(1)Aiming at the problem that tensor nuclear norms based on t-SVD ignore the significant information between singular values and the low-rank description cannot well describe the correlations and category geometry in the data,this chapter proposes robust principal com-ponent analysis based on weighted tensor Schatten p-Norm.The model explicitly considers the difference information of the singular values when solving the low-rank description,and improves the robustness of the low-rank description.Based on this,an effective solution algorithm and convergence analysis are given.And theoretical analysis shows that several existing low-rank description models are special cases of the models proposed in this chap-ter.(2)Multi-view clustering methods based on tensor nuclear norm use the same shrinking strategy for all singular values,ignoring the differences of singular values,which leads to the problem that the self-expression coefficient matrix cannot accurately characterize the category structure of the data.This chapter proposes multi-view subspace clustering based on weighted tensor Schatten p-Norm model,and uses Alternating Direction Minimiz-ing(ADM)method to optimize the model.Simulation experiments on databases of faces,objects,scenes,etc.all show the effectiveness of the algorithm proposed in this chapter.(3)Multi-view subspace clustering based on weighted tensor Schatten p-Norm only consid-ers the low-rank structure of the subspace tensors constructed in all views,and ignores the local structure information in each view.So the clustering performance is limited.Aiming at this problem,this chapter proposes Multi-view Sparse Subspace Clustering Based Weight Tensor Schatten p-Norm model.This method simultaneously minimizes the l₁norm of the self-expression coefficient matrix in each view and the weighted tensor Schatten p-Norm of the subspace tensor.So the learned shared self-expression coefficient matrix can better char-acterize the class geometry.At the same time,this chapter uses ADM method to effectively optimize the model.The experimental results on multiple data sets prove the superiority of the algorithm and good convergence.