Subspace Clustering Based On Sparse Representation

In today's society,due to the development of science and technology,all aspects of production and life generate massive amounts of data,and their full use will generate huge value for human society.However,the high dimension of data and the complexity of structure give data Analysis,processing,and storage pose challenges.Subspace clustering is a brand-new data clustering method.It divides high-dimensional data into several low-dimensional subspaces,where each subspace corresponds to a class,which is convenient for data analysis and processing.As an effective data analysis and processing scheme,subspace clustering has been widely used in the fields of machine learning,computer vision,image processing and system recognition.The subspace clustering method based on spectral clustering is mainly divided into two steps: first,the coefficient matrix is obtained by using the sparse representation of high-dimensional data,and secondly,the similarity matrix is constructed;finally,the subspace clustering of the data is obtained by using spectral clustering method Category result.The structure of the similarity matrix basically determines the performance of clustering.Existing methods use various regular methods to constrain the data self-representation coefficient matrix so that it has a structure that is beneficial to clustering.Although the subspace clustering algorithm has been extensively explored,there are still many problems that need to be improved.Based on the sparse representation,this paper studies the subspace clustering of high-dimensional data,mainly considers the correlation between data and data,the global structure of data and the internal geometric structure of data,and designs a more effective subspace clustering model.This paper mainly studies the subspace clustering model based on block diagonal sparse.The research results include: introducing orthogonal matrix into the block diagonal sparse regularization,and improving the block diagonal representation subspace clustering(BDR)model to relaxation Block diagonal subspace clustering(RBDR)model,which forces the self-representation matrix to conform to the block diagonal structure,while allowing the self-representation matrix to have an orthogonal matrix difference;The local similarity is introduced into the model to participate in the global similarity solution.The weighted matrix based on the sample local similarity is used to enhance the block diagonal structure of the self-representation coefficient matrix.The RBDR model is improved to a relaxation weighted block diagonal subspace clustering(RWBDR)model.Using this model to obtain the coefficient matrix can better present the similarity between data points;this paper also proposes another minimization algorithm to solve the RBDR model and RWBDR model.Experiments on multiple public data sets show that the new model presented in this paper effectively improves the performance of the BDR model,especially when the data is not arranged by class,and most of the data to be clustered in reality is so.