Cascade subspace clustering

Abstract

In this paper, we recast the subspace clustering as a verification problem. Our idea comes from an assumption that the distribution between a given sample x and cluster centers Ω is invariant to different distance metrics on the manifold, where each distribution is defined as a probability map (i.e. soft-assignment) between x and Ω. To verify this socalled invariance of distribution, we propose a deep learning based subspace clustering method which simultaneously learns a compact representation using a neural network and a clustering assignment by minimizing the discrepancy between pair-wise sample-centers distributions. To the best of our knowledge, this is the first work to reformulate clustering as a verification problem. Moreover, the proposed method is also one of the first several cascade clustering models which jointly learn representation and clustering in end-to-end manner. Extensive experimental results show the effectiveness of our algorithm comparing with 11 state-of-the-art clustering approaches on four data sets regarding to four evaluation metrics.