A kurtosis-based dynamic approach to Gaussian mixture modeling

We address the problem of probability density function estimation using a G aussian mixture model updated with the expectation-maximization (EM) algori thm. To deal with the case of an unknown number of mixing kernels, we defin e a new measure for Gaussian mixtures, called total kurtosis, which is base d on the weighted sample kurtoses of the kernels. This measure provides an indication of how well the Gaussian mixture fits the data. Then we propose a new dynamic algorithm for Gaussian mixture density estimation which monit ors the total kurtosis at each step of the Ehl algorithm in order to decide dynamically on the correct number of kernels and possibly escape from loca l maxima. We show the potential of our technique in approximating unknown d ensities through a series of examples with several density estimation probl ems.