Research On Multi-view Clustering Algorithm Based On Low-rank And Sparse Constraints

With the rapid development of information technology,multi-view data has emerged due to the different descriptions of things from different views.Currently,when analyzing multi-view data,the methods of single-view clustering often produce suboptimal clustering results due to the neglect of correlation information among views.In response to this issue,a multi-view clustering method has been developed that takes into account information such as relevance and differences among views.In multi-view clustering methods,subspace clustering algorithms based on low-rank and sparse constraints can capture relevant features of both the global and local structures of data,and thus obtain better clustering results.However,existing multi-view clustering methods based on low-rank and sparse constraints generally suffer from two problems:(1)In the process of multi-view clustering,methods that approximate the rank function of self-representation matrix based on the nuclear norm and the gamma norm are greatly influenced by the singular values of matrix and critical breakpoints of function,respectively;(2)When fusing original data in the data domain,the learned common representation matrix directly on the data domain cannot take into account the differences among various views due to the large differences among multi-view data.Therefore,this thesis aims to address the above two key problems,and the research content involved is as follows:1.To address the issue of the existing methods that approximate the rank function of self-representation matrix based on the nuclear norm and the gamma norm,which are greatly influenced by the singular values of matrix and critical breakpoints of function,this thesis proposes a non-convex relaxation method for low-rank constraint of the self-representation matrix by utilizing techniques such as block inversion in unitary matrix processing to obtain a more accurate approximation of the rank function.At the same time,an adaptive weight method is used to allocate reasonable weights for each view to solve the problem of the large differences among multi-view data that affect the learning of the common representation matrix.Finally,this thesis conducts relevant experiments on five multi-view datasets using the proposed low-rank approximation method,and compares the experimental results of this method with the average results of other mainstream low-rank approximation methods.The experimental results show that the proposed low-rank approximation method can obtain 3.23%improvement in the F-score of the UCI Digit dataset.2.To address the issue of the common representation matrix learned from directly fusing the data from different views in the data domain cannot take into account the differences among various views,this thesis proposes a multi-view clustering method based on the fusion of spectral structure by utilizing the conclusion that the spectral structure corresponding to each view data is relatively similar.This method can learn the common representation matrix on the spectral structure corresponding to the original data,which can fully consider the differences among various views and improve the clustering performance.Finally,this thesis conducts relevant experiments on five multi-view datasets using the proposed spectral structure fusion method,and compares the experimental results of this method with the average results of existing mainstream multi-view clustering methods.The experimental results show that the proposed spectral structure fusion method can obtain 2.37%improvement in the F-score of the 3-sources dataset.