Multi-view clustering by joint manifold learning and tensor nuclear norm

Abstract

In real-world applications, the variation between multi-view data points, which should belong to the same cluster, is larger than the variation between data points belonging to different clusters. This results in instability of most existing clustering algorithms, because they mainly employ the original data as input to learn the latent similarity matrix. To address these problems, we propose a novel latent similarity learning for multi-view clustering(LSLMC) by integrating manifold learning and tensor Singular Value Decomposition (t-SVD) into a uniform framework. LSLMC utilizes the similarity matrices calculated from each view to recover a latent representation matrix by local manifold learning coupled with spectral clustering. Thus, the adaptively recovered similarity matrix, which is shared by all views, can well characterize both the clustering structure and local manifold structure underlying multi-view data. In addition, by simultaneously using low-rank tensor constraint on the error matrix, the view-specific information and the noise can be well explored. Therefore, the recovered similarity matrix become more robust and accurate, leading to better clustering performance. Extensive experiments on five widely used multi-view datasets have demonstrated the superiority of the proposed method.