Two iterative algorithms for maximum likelihood esitimation of Gaussian mixture parameter

Gaussian mixture is a typical and widely-used non-Gaussian probability density distribution model. Its parameter´s efficient estimation is the maximum likelihood estimation. The expectation-maximization algorithm is an usual iterative realization for this maximum likelihood estimation. However, its performance depends highly on the initial values. The greedy expectation-maximization algorithm can solve this problem efficiently by incrementally adding Gaussian components to the mixture. However, with appropriate initialization, the former can converge at the correct value quickly than the later. The concrete realization method of these two iterative algorithms is given. A numerical simulation illustrates their performance.