A Q-EM Based Simulated Annealing Algorithm for Finite Mixture Estimation

We develop a q-expectation maximization (q-EM) simulated annealing method for parameter estimation. The g-EM algorithm is a one-parameter generalization of normal expectation maximization (EM) algorithm based on Tsallis entropy. By incorporating the simulated annealing method, we propose the q-deterministic annealing expectation maximization (q-DAEM) algorithm. Given the inherent connection between a physical annealing process and statistical mechanics, we show that the proposed algorithm actually minimizes a counterpart of the free energy in statistical mechanics by controlling an effective temperature. Simulations of mixed Gaussian parameter estimation show that the proposed method is much less initialization-dependent than the standard EM algorithm and converges dramatically faster than the DAEM algorithm.