Distance-Based Probability Distribution for Set Partitions with Applications to Bayesian Nonparametrics

Integration of several types of data is a burgeoning field. Some data naturally lead to formal models; others may convey proximity among observations. Clustering methods are typically either model-based or distanced-based, but not both. We propose a method that is simultaneously model-based and distance-based, permitting the use of both types of data. We show the Dirichlet process induces a clustering distribution in which the probability that an item is clustered with another item is uniform across all items. We provide an extension which incorporates distance information to provide a probability distribution for partitions that is indexed by pairwise distances between items. We show how to utilize this new distance-based probability distribution over partitions as a prior clustering distribution in Bayesian nonparametric models. We show an application to ion mobility-mass spectrometry.

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