Semi-supervised Clustering using Combinatorial MRFs

A combinatorial random variable is a discrete random variable defined over a combinatorial set (e.g., a power set of a given set). In this paper we introduce combinatorial Markov random fields (Comrafs), which are Markov random fields where some of the nodes are combinatorial random variables. We argue that Comrafs are powerful models for unsupervised learning by showing their relationship with two existing models. We then present a Comraf model for semi-supervised clustering that demonstrates superior results in comparison to an existing semi-supervised scheme (constrained optimization).