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The fundamental aim of clustering algorithms is to partition data points. Weconsider tasks where the discovered partition is allowed to vary with somecovariate such as space or time. One approach would be to usefragmentation-coagulation processes, but these, being Markov processes, arerestricted to linear or tree structured covariate spaces. We define apartition-valued process on an arbitrary covariate space using Gaussianprocesses. We use the process to construct a multitask clustering model whichpartitions datapoints in a similar way across multiple data sources, and a timeseries model of network data which allows cluster assignments to vary overtime. We describe sampling algorithms for inference and apply our method todefining cancer subtypes based on different types of cellular characteristics,finding regulatory modules from gene expression data from multiple humanpopulations, and discovering time varying community structure in a socialnetwork.

A dependent partition-valued process for multitask clustering and time evolving network modelling