$k$-MLE: A fast algorithm for learning statistical mixture models

We present a fast and generic algorithm, k-MLE, for learning statistical mixture models using maximum likelihood estimators. We prove theoretically that k-MLE is dually equivalent to a Bregman k-means for the case of mixtures of exponential families (e.g., Gaussian mixture models). k-MLE is used to initialize appropriately the expectation-maximization algorithm. We also show experimentally that k-MLE outperforms the EM technique with standard initialization by considering modeling color images using high-dimensional Gaussian mixture models.