Learning Graph Similarity With Large Spectral Gap

Abstract

Learning a good graph similarity matrix in data clustering is very crucial. The goal of clustering is to construct a good graph similarity matrix such that the similarity of points between the same classes is largest, and the similarity of points between different classes is smallest. In this paper, a more efficient subspace segmentation approach to learn a similarity matrix with large spectral gap is proposed. In our model, a robust self-representation coefficient matrix is learned by utilizing the Schatten- ${p}$ norm instead of the conventional rank function. Besides, the fast block-diagonal structure of the coefficient representation matrix is enhanced by learning and optimizing the co-association matrix with the soft label of clustering results simultaneously in a unified framework. The affinity graphs constructed in this paper can clearly reveal the intrinsic structures of the data sets. Extensive experiments on the real data sets demonstrate that our proposed method can perform better than the state-of-the-art methods.