Semisupervised learning of mixture models with class constraints

Most prior work on semisupervised clustering/mixture modeling with given class constraints assumes the number of classes is known, with each learned cluster assumed to be a class and, hence, subject to the given instance-level constraints. When the number of classes is incorrectly assumed and/or when the "one-cluster-perclass" assumption is not valid, the use of constraint information in these methods may actually be deleterious to learning the ground-truth data groups. In this work we extend semisupervised learning with constraints 1) to allow allocation of multiple mixture components to individual classes and 2) to estimate both the number of components/clusters and, leveraging the constraint information, the number of classes present in the data. For several real-world data sets, our method is shown to correctly estimate the number of classes and to give a favorable comparison with the recent mixture modeling approach of Shental et al.