Learning a Joint Affinity Graph for Multiview Subspace Clustering

With the ability to exploit the internal structure of data, graph-based models have received a lot of attention and have achieved great success in multiview subspace clustering for multimedia data. Most of the existing methods individually construct an affinity graph for each single view and fuse the result obtained from each single graph. However, the common representation shared by different views and the complementary diversity across these views are not efficiently exploited. In addition, noise and outliers are often mixed in original data, which adversely degenerate the clustering performance of many existing methods. In this paper, we propose addressing these issues by learning a joint affinity graph for multiview subspace clustering based on a low-rank representation with diversity regularization and a rank constraint. Specifically, a low-rank representation model is employed to learn a shared sample representation coefficient matrix to generate the affinity graph. At the same time, we use diversity regularization to learn the optimal weights for each view, which can suppress the redundancy and enhance the diversity among different feature views. In addition, the cluster number is used to promote affinity graph learning by using a rank constraint. The final clustering result is obtained by using normalized cuts on the learned affinity graph. An efficient algorithm based on an augmented Lagrangian multiplier with alternating direction minimization is carefully designed to solve the resulting optimization problem. Extensive experiments on various real-world datasets are conducted, and the results demonstrate well the effectiveness of the proposed algorithm.