  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.
