A Gibbs Sampler for Spatial Clustering with the Distance-dependent Chinese Restaurant Process

The distance-dependent Chinese Restaurant Process (dd-CRP) is a flexible class of distributions over partitions which was recently introduced by [1, 2]. In their description and experiments Blei and Frazier focus on the sequential setting such as clustering over time. Their Gibbs sampler, while general in nature, does not explicitly handle the case of non-sequential (also called spatial) clustering. In this case further details are needed for a correct implementation. We introduce the Gibbs sampler for spatial clustering with the dd-CRP. For simplicity, we focus on infinite Gaussian mixture models (IGMM) [9].