EVM: A Fast Alternative to the EM Algorithm with Application to Gaussian Mixture Models

This article presents EVM (Expectation-Variance-Maximization) — an alternative algorithm to the EM algorithm that can reduce training times dramatically. The new approach belongs to the class of general Newton algorithms and is applicable in most situations where the EM algorithm is currently used so is useful for a wide variety of estimation problems. Two identities associated with the EM algorithm provide analytical expressions for the gradient and Hessian matrices used in the EVM algorithm. The new algorithm is demonstrated for parameter estimation in Gaussian Mixture Models. Simulations show that training times are reduced significantly and in difficult cases more than 100-fold in comparison to the EM algorithm.