Batch and on-line parameter estimation of Gaussian mixtures based on the joint entropy

We describe a new iterative method for parameter estimation of Gaussian mixtures. The new method is based on a framework developed by Kivinen and Warmuth for supervised on-line learning. In contrast to gradient descent and EM, which estimate the mixture's covariance matrices, the proposed method estimates the inverses of the covariance matrices. Furthermore, the new parameter estimation procedure can be applied in both on-line and batch settings. We show experimentally that it is typically faster than EM, and usually requires about half as many iterations as EM.