K-means and gaussian mixture modeling with a separation constraint

We consider the problem of clustering with K-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the K-means problem with a separation constraint on the centers, building on Wang and Song (2011). In the context of fitting a Gaussian mixture model, we then propose an EM algorithm that incorporates such a constraint. A separation constraint can help regularize the output of a clustering algorithm, and we provide both simulated and real data examples to illustrate this point.