Abstract
Finite mixture models (FMMs) are an indispensable tool for unsupervised classification in brain imaging. Fitting an FMM to the data leads to a complex optimization problem. This optimization problem is difficult to solve by standard local optimization methods such as the expectation maximization (EM) algorithm if a good initialization is not available. In this paper, we propose a new global optimization algorithm for the FMM parameter estimation problem, which is based on the real coded genetic algorithms. Our specific contributions are two-fold: 1) We propose to use blended crossover in order to reduce the premature convergence problem to its minimum. 2) We introduce a completely new permutation operator specifically meant for the FMM parameter estimation. In addition to the improving the optimization results, the permutation operator allows for imposing biologically meaningful constraints to the FMM parameter values. We also introduce a hybrid of the genetic algorithm and the EM algorithm for efficient solution of multi-dimensional FMM fitting problems. We demonstrate the good behavior of our algorithm compared to the self annealing EM-algorithm and a standard real coded genetic algorithm with the voxel classification tasks within the brain imaging. The algorithms are tested on synthetic data as well as real three dimensional image data from human magnetic resonance imaging (MRI), positron emission tomography, and mouse brain MRI. The tissue classification results by our method are shown to be consistently more reliable and accurate than with the competing parameter estimation methods.