Estimating time-varying densities using a stochastic learning automaton

The popular Expectation Maximization technique suffers a major drawback when used to approximate a density function using a mixture of Gaussian components; that is the number of components has to be a priori specified. Also, Expectation Maximization by itself cannot estimate timevarying density functions. In this paper, a novel stochastic technique is introduced to overcome these two limitations. Kernel density estimation is used to obtain a discrete estimate of the true density of the given data.A Stochastic Learning Automaton is then used to select the number of mixture components that minimizes the distance between the density function estimated using the Expectation Maximization and discrete estimate of the density. The validity of the proposed approach is verified using synthetic and real univariate and bivariate observation data.