Model-based Clustering With Probabilistic Constraints

The problem of clustering with constraints is receiving increasing attention. Many existing algorithms assume the specified constraints are correct and consistent. We take a new approach and model the uncertainty of constraints in a principled manner by treating the constraints as random variables. The effect of specified constraints on a subset of points is propagated to other data points by biasing the search for cluster boundaries. By combining the a posteriori enforcement of constraints with the log-likelihood, we obtain a new objective function. An EM-type algorithm derived by variational method is used for efficient parameter estimation. Experimental results demonstrate the usefulness of the proposed algorithm. In particular, our approach can identify the desired clusters even when only a small portion of data participates in constraints.