On unsupervised clustering under the union of tensor subspaces

In this paper we consider the problem of unsupervised clustering under a union of tensor (multilinear) subspaces model. In particular we take the popular union of subspaces model and endow the subspaces with an additional algebraic structure, namely that each subspace is a is a tensor product of subspaces. The resulting model is referred to as the union of tensor or multilinear subspaces. We show that several real world data sets such as images and action video data sets can be effectively represented using this model. Under this model we investigate an algorithm referred to as the Multilinear Subspace Clustering (MSC). In this context we first show by simulations on synthetic data that MSC is computationally more efficient compared to several existing methods indicating its utility in dealing with high dimensional data. Further we compare the clustering performance of the algorithm on several real-world data sets and show that MSC is competitive with current state-or-art methods. Based on these results we point out future research directions in using the multilinear/tensor algebraic framework for big-data processing.