Consensus Affinity Graph Learning via Structure Graph Fusion and Block Diagonal Representation for Multiview Clustering

Learning a robust affinity graph is fundamental to graph-based clustering methods. However, some existing affinity graph learning methods have encountered the following problems. First, the constructed affinity graphs cannot capture the intrinsic structure of data well. Second, when fusing all view-specific affinity graphs, most of them obtain a fusion graph by simply taking the average of multiple views, or directly learning a common graph from multiple views, without considering the discriminative property among diverse views. Third, the fusion graph does not maintain an explicit cluster structure. To alleviate these problems, the adaptive neighbor graph learning approach and the data self-expression approach are first integrated into a structure graph fusion framework to obtain a view-specific structure affinity graph to capture the local and global structures of data. Then, all the structural affinity graphs are weighted dynamically into a consensus affinity graph, which not only effectively incorporates the complementary affinity structure of important views but also has the capability of preserving the consensus affinity structure that is shared by all views. Finally, a k-block diagonal regularizer is introduced for the consensus affinity graph to encourage it to have an explicit cluster structure. An efficient optimization algorithm is developed to tackle the resultant optimization problem. Extensive experiments on benchmark datasets validate the superiority of the proposed method.