Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

224921

Hartigan's method for $$$$-mle

mixture modeling with wishart distributions and its application to motion retrieval

Christophe Saint-JeanFrank Nielsen

pp. 301-330

Abstract

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.

Publication details

Published in:

Nielsen Frank (2014) Geometric theory of information. Dordrecht, Springer.

Pages: 301-330

DOI: 10.1007/978-3-319-05317-2_11

Full citation:

Saint-Jean Christophe, Nielsen Frank (2014) „Hartigan's method for $$$$-mle: mixture modeling with wishart distributions and its application to motion retrieval“, In: F. Nielsen (ed.), Geometric theory of information, Dordrecht, Springer, 301–330.