Clustering on the Stiefel Manifold with Symmetric Block Term Decomposition

In this paper, we consider the problem of clustering a collection of tall matrices with respect to their partially “common” column spaces. We show that the considered problem is closely related to Subspace Clustering and Generalized Canonical Correlation Analysis, while it can be posed in terms of the Block Term Decomposition of a tensor. In order to address instances of this problem, we propose an optimization algorithm for learning the memberships and the partially “common” subspaces. We compare the proposed approach to several state of the art Subspace Clustering methods using synthetic data and demonstrate the superiority of the proposed method in terms of performance and robustness to strong noise and interference.