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

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.