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Semi-supervised clustering is the task of clustering data points intoclusters where only a fraction of the points are labelled. The true number ofclusters in the data is often unknown and most models require this parameter asan input. Dirichlet process mixture models are appealing as they can infer thenumber of clusters from the data. However, these models do not deal with highdimensional data well and can encounter difficulties in inference. We present anovel nonparameteric Bayesian kernel based method to cluster data pointswithout the need to prespecify the number of clusters or to model complicateddensities from which data points are assumed to be generated from. The keyinsight is to use determinants of submatrices of a kernel matrix as a measureof how close together a set of points are. We explore some theoreticalproperties of the model and derive a natural Gibbs based algorithm with MCMChyperparameter learning. The model is implemented on a variety of synthetic andreal world data sets.

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