Applying fuzzy EM algorithm with a fast convergence to GMMs

Inspired from the mechanism of Fuzzy C-means (FCMs) which introduces a degree of fuzziness on the dissimilarity function based on distances, a fuzzy Expectation Maximization (EM) algorithm for Gaussian Mixture Models (GMMs) is proposed in this paper. In the fuzzy EM algorithm, the dissimilarity function is defined as the multiplicative inverse of probability density function. Different from FCMs, the defined dissimilarity function is based on the exponential function of the distance. The fuzzy EM algorithm is compared with normal EM algorithm in terms of fitting degree and convergence speed. The experimental results in modeling random data and various characters demonstrate the ability of the proposed algorithm in reducing the computational cost of GMMs.