Research On Subspace Clustering Algorithm Based On Graph Regularization

Subspace clustering is an extension of the traditional clustering problem,the purpose of which is to segment the data points lying on the union of multiple subspaces into corresponding subspaces.Sparse subspace clustering(SSC)and low-rank representation(LRR)are the two most representative subspace clustering algorithms.In order to obtain a more ideal coefficient matrix,a subspace clustering algorithm based on graph regularization is proposed in this paper.The basic method of the subspace clustering algorithm is to establish a model to seek the ideal coefficient matrix,solve the coefficient matrix by the augmented Lagrange multiplier method,then use the coefficient matrix to construct the similarity matrix,and finally use the spectral clustering method to get clustering results.The main contributions of this article are as follows:1)Laplacian embedded sparse subspace clustering algorithm(L-SSC)is proposed.Unlike SSC,which uses the sparse representation of the coefficient matrix as a regularization term,the regularization term of L-SSC is the sparse representation of the Laplacian embedded quadratic term.This regularization term contains the similarity between the data vectors and forces the coefficient matrix to have a more sparse structure.In addition,we also introduce an additional penalty term to capture the sequential properties of the data matrix,which can eliminate the instability and increase the smoothness of the model.2)A low-rank representation algorithm(GR-LRR)based on graph regularization is proposed.The L-LRR algorithm seeks a low-rank representation of a graph regularization term with a Laplacian matrix,and uses the nature of the graph regularization term to capture the internal structure of the data,thereby increasing the weight of the coefficients corresponding to inter-clustering samples and reducing the weight of the coefficients corresponding to intra-clustering samples.In order to obtain a coefficient matrix with a more ideal geometric structure,we also impose a symmetric constraint on the coefficient matrix to ensure the consistency of the weights of the paired data points.Finally,we use the angle information of the principal direction of the symmetric low-rank coefficient matrix to construct a similarity matrix.3)A low-rank sparse subspace clustering algorithm(GR-LRSSC)based on graph regularization is proposed.The GR-LRSSC algorithm is a combination of the above two algorithms.A subspace clustering algorithm based on graph regularization is applied to the low-rank sparse representation framework aiming to combine the advantages of sparse representation and low-rank representation.GR-LRSSC can avoid the representation matrix is over-sparse and capture the global structure of the data.