Research Of Self-representation Subspace Clustering Algorithm

Cluster analysis is one of the important research methods in the field of data mining.Its main goal is to divide the samples of a data set into different categories without prior information,so that the similarity of samples in the same category is as large as possible and the sample difference within the different category is as large as possible.Clustering has the characteristics of unsupervised learning,so it has been widely used in many fields.However,traditional clustering algorithms,affected by the "dimension disaster",are often unsatisfactory when processing high-dimensional data.The subspace clustering algorithm is an extension of the traditional clustering algorithm on high-dimensional data.Its basic idea is to divide the original data space into different subspaces and look for the possibility of different categories in the subspace.However,subspace clustering algorithms have problems that they are difficult to maintain the nonlinearity and local geometric structure of data.In response to these problems,this paper conducts research on self-representation subspace clustering algorithm.The main research results are as follows:(1)Scaled Simplex Representation for Subspace Clustering(SSRSC)guarantees the sparsity of coefficient matrix by controlling coefficient matrix vector sum.However,the algorithm is inadequately considered the local geometric structure of data.To solve this problem,Scaled simplex Representation and Graph regularization for Subspace Clustering(SRGSC)is proposed.Under the framework of SSRSC,the graph regularization term is introduced.SRGSC uses Laplacian feature mapping to obtain the local manifold structure of data and then uses k-nearest neighbor graph to influence the generation of coefficient matrix,solving SRGSC by Alternating Direction Multiplier Method.Experiments on artificial datasets,UCI datasets and image datasets show that SRGSC can achieve better performance.(2)Subspace Clustering by Block Diagonal Representation(BDR)proposes k-block diagonal regular terms to directly constrain the block-diagonal structure of coefficient matrix.However,this algorithm forces coefficient matrix to be equal to its transposed matrix,so that coefficient matrix satisfies the condition of positive definite symmetry.Therefore,the sample points lose their self-representation ability,which leads to poor clustering effect of this algorithm on high-dimensional data.In response to this problem,quadratic programming regular term introduced,this paper proposes Subspace clustering Quadratic programming by Block Diagonal Representation(SQBDR).The quadratic programming regular term is used to constrain coefficient matrix positive definite,while enhancing the diagonal structure of its block and increasing its sparsity.Experimental results on different data sets verify the effectiveness of SQBDR for clustering problems.