DP-Space: Bayesian Nonparametric Subspace Clustering with Small-Variance Asymptotics

Abstract

Subspace clustering separates data points approximately lying on union of affine subspaces into several clusters. This paper presents a novel nonparametric Bayesian subspace clustering model that infers both the number of subspaces and the dimension of each subspace from the observed data. Though the posterior inference is hard, our model leads to a very efficient deterministic algorithm, DP-space, which retains the nonparametric ability under a small-variance asymptotic analysis. DP-space monotonically minimizes an intuitive objective with an explicit tradeoff between data fitness and model complexity. Experimental results demonstrate that DP-space outperforms various competitors in terms of clustering accuracy and at the same time it is highly efficient.