Subspace Clustering By Block Diagonal Affinity Matrix

In recent years,subspace clustering methods based on spectral clustering have become a research hotspot.Many methods of subspace clustering have been proposed,and the low-rank representation(LRR)and sparse subspace clustering(SSC)are two classical methods.Both of them employ the self-representation of raw data to extract the relationship between the data set,when the data sampling is sufficient and the subspaces are independent,the resulting representation coefficient matrices are both block-diagonal,and the number of diagonal blocks is equal to the number of categories in the data set.As LRR and SSC are proposed,representation coefficient matrices of the extensions of these two classical clustering methods are usually block-diagonal,too.In summary,the block diagonal property plays a key role in whether the data can be correctly clustered.Therefore,subspace clustering by block diagonal representation(BDR)is proposed.In this method,the block diagonal regularization term is used to ensure that the coefficient matrix is diagonal.However,BDR requires the representation coefficient matrix to be non-negative and symmetry for the solution of the model,these constraints will limit the ability of the coefficient matrix mining relationship between the data set.To overcome the limitation of BDR,since the affinity matrix is non-negative and symmetric,we add the block diagonal regularization for the affinity matrix and propose a subspace clustering method based on the block diagonality of the affinity matrix.Our proposed method no longer limits the representation ability of the representation coefficient matrix,but also guarantees the block diagonality of the affinity matrix to improve the clustering performance.However,penalizing the affinity matrix will make the model difficult to solve.Fortunately,we successfully design the numerical algorithm,and conduct experiments on multiple datasets to verify the effectiveness of our proposed method.