Pearson and intra-inter-class weighted block diagonal representation learning for subspace clustering

Abstract

Block diagonal is an important characteristic of the self-expression coefficient matrix in subspace clustering. However, the global constraint on the self-expression coefficient matrix suffers from the impact of inter-class similarity and the intra-class dissimilarity, as well as the disturbance of noise. To facilitate subspace clustering by enhancing the representation ability of the self-expression coefficient matrix, we propose an enhanced block diagonal representation(BDR) learning that considers internal and external data correlations from the perspectives of pairwise and classwise correlation. First, Pearson correlation is employed to describe local pairwise similarities and acts as a weight to strengthen the corresponding connections between pairwise data points in the self-expression coefficient matrix. Then, a unified intra-class and inter-class dissimilarity constraint is proposed to increase the coefficient values of the same class and decrease the coefficient values of different classes, in other words, enhance intra-class compactness and inter-class separability at the classwise level. In this way, a multi-level constraint on the self-expression coefficient matrix is proposed, from pairwise to classwise along with the global-wise BDR constraint. Experimental results show that the block diagonal structure of the self-expression coefficient matrix is significantly improved with these two additional constraints. Further, with the enhanced self-expression coefficient matrix, the accuracies of the clustering results are also improved.