A new EM algorithm using Tikhonov regularization

Abstract

A new expectation-maximization (EM) algorithm which employs Tikhonov regularization is proposed. In this paper we use the new algorithm to estimate the parameters of a Gaussian mixture model. Two learning steps are involved: first the standard EM algorithm is used to get an initial estimate of the parameters; next, a regularized version of the EM algorithm is used to improve the smoothness and generalization properties of the estimated density function. To illustrate the effectiveness of the approach, both the standard EM algorithm and the new regularized EM algorithm are compared in a density estimation task, using an artificial dataset. The results clearly indicate that the regularized EM algorithm leads to better estimates in terms of smoothness and generalization capabilities.