A note on the optimal scalar Bregman k-means clustering with an application to learning best statistical mixtures

We describe a dynamic programming (DP) technique to compute the optimal Bregman k-means clustering of $n$ scalar values. We further show how to incorporate constraints on the minimum sizes of clusters. We then illustrate how to use this DP algorithm for learning univariate statistical mixture models of exponential families maximizing the complete data likelihood, and perform model selection from the DP table.