Determinantal Clustering Process- A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clus-tering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often un-known and most models require this param-eter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimen-sional data well and can encounter difficulties in inference. We present a novel nonparame-teric Bayesian method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel ma-trix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyper-parameter learning. We test the model on various synthetic and real world data sets.