DP-space: Bayesian Nonparametric Subspace Clustering with Small-variance Asymptotics

Subspace clustering separates data points ap-proximately lying on union of affine subspaces into several clusters. This paper presents a novel nonparametric Bayesian subspace cluster-ing model that infers both the number of sub-spaces and the dimension of each subspace from the observed data. Though the posterior infer-ence is hard, our model leads to a very effi-cient deterministic algorithm, DP-space, which retains the nonparametric ability under a small-variance asymptotic analysis. DP-space mono-tonically 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. 1