Hartigan’s method for k-MLE : Mixture modeling with Wishart distributions and its application to motion retrieval

We describe a novel algorithm called k-Maximum Likelihood Estimator (k-MLE) for learning finite statistical mixtures of exponential families relying on Hartigan’s k-means swap clustering method. To illustrate this versatile Hartigan k-MLE technique, we consider the exponential family of Wishart distributions and show how to learn their mixtures. First, given a set of symmetric positive definite observation matrices, we provide an iterative algorithm to estimate the parameters of the underlying Wishart distribution which is guaranteed to converge to the MLE. Second, two initialization methods for k-MLE are proposed and compared. Finally, we propose to use the Cauchy-Schwartz statistical divergence as a dissimilarity measure between two Wishart mixture models and sketch a general methodology for building a motion retrieval system.