A $q$-Parameterized Deterministic Annealing EM Algorithm Based on Nonextensive Statistical Mechanics

摘要

We propose a $q$ -parameterized deterministic annealing expectation maximization ($q$-DAEM) algorithm for parameter estimation motivated by the concept of Tsallis entropy that originates from the nonextensive statistical mechanics. The $q$-DAEM algorithm combines the feature of annealing algorithms to reduce initialization sensitivity and that of $q$-EM algorithms to achieve fast convergence. The $q$-EM algorithm is a one-parameter generalized EM algorithm that has been previously proposed by the authors. By interpreting the EM algorithm via likelihood lower bound maximization, we build the fundamental interconnections among DAEM, $q$-DAEM, and statistical mechanics. To illustrate the benefits of using $q$-DAEM, we investigate two applications: finite mixture model estimation in data clustering; and joint channel estimation and data detection in communication systems, where we show that the $q$-DAEM algorithm achieves superior performance over the EM algorithm for both applications.