Abstract
Multi-way data or tensors are generalizations of matrices. Clustering multi-way data is a very important research topic due to the intrinsic rich structures in real-world datasets. Despite significant progress made on subspace clustering for two-way data, few attempts have been made to develop subspace clustering algorithms on multi-way data. In this paper, we propose the subspace clustering algorithm on multi-way data, called ASI-T (Adaptive Subspace Iteration on Tensor). We show that ASI-T is a special version of High Order SVD (HOSVD), a commonly used tensor factorization method. We show that ASI-T is simultaneously performing subspace identification using 2DSVD (identifying the subspace structure of the tensor from the current data clusters) and data clustering using K-Means (clustering the data units on the current identified subspaces). By explicitly modeling subspace structures, ASI-T is also able to generate interpretable clustering results. The experimental results on both synthetic data and real-world data demonstrate the effectiveness of ASI-T.