Multi-view clustering with adaptive procrustes on Grassmann manifold

Multi-view clustering plays an important role in a wide spectrum of applications. In this article, we propose a multi-view clustering approach with adaptive Procrustes on Grassmann manifold (MC-APGM) to overcome the three demerits in existing graph-based multi-view clustering methods, namely, insufficient mining of subspace information of views, a requirement for post-processing, and high computational complexity. Specifically, in the proposed model, the indicator matrix is directly learned from multiple orthogonal spectral embeddings, avoiding the random clustering results caused by post-processing; The orthogonal form of the indicator matrix approximates multiple orthogonal spectral embeddings on the Grassmann manifold, fully uncovering subspace information of views and thus improving clustering performance; Both implicitly and explicitly weighted learning mechanisms are established to capture inconsistencies among different views. Moreover, an efficient algorithm with rigorous convergence guarantee is derived to optimize the proposed model. Finally, experimental results on both toy and real-world datasets demonstrate the effectiveness and efficiency of this proposed method.