Learning a consensus affinity matrix for multi-view clustering via subspaces merging on Grassmann manifold

Abstract Integrative multi-view subspace clustering aims to partition observed samples into underlying clusters through fusing representative subspace information from different views into a latent space. The clustering performance relies on the accuracy of sample affinity measurement. However, existing approaches leverage the subspace representation of each view and overlook the learning of appropriate sample affinities. This paper proposes to learn a consensus affinity directly by merging subspace representations of different views on a Grassmann manifold while maintaining their geometric structures across these views. The proposed method not only preserves the structure of the most informative individual view, but also discovers a latent common structure across all views. The associated constrained optimization problem is solved using the alternating direction method of multipliers. Extensive experiments on synthetic and real-world datasets show that the proposed method outperforms several state-of-the-art multi-view subspace clustering methods. The affinity matrix obtained by our method can extract highly representative and latent common information to enhance the clustering performance.