A Genetic EM Algorithm for Learning the Optimal Number of Components of Mixture Models

Mixture models have been widely used in cluster analysis. Traditional mixture densities-based clustering algorithms usually predefine the number of clusters via random selection or contend based knowledge. An improper pre-selection of the number of clusters may easily lead to bad clustering outcome. Expectation-maximization (EM) algorithm is a common approach to estimate the parameters of mixture models. However, EM is prone to converge into local maximum after a limited number of iterations. Moreover, EM usually assumes that the number of mixing components is known in advance, which is not always the case in practice. In order to address these issues we propose in this paper a new genetic EM algorithm to learn the optimal number of components of mixture models. Specifically, the algorithm defines an entropy-based fitness function, and two genetic operators for splitting and merging components. We conducted two sets of experiments using a synthetic dataset and two existing benchmarks to validate our genetic EM algorithm. The results obtained in the first experiment show that the algorithm can estimate exactly the optimal number of clusters for a set of data. In the second experiment, we computed three major clustering validity indices and compared the corresponding results with those obtained using established clustering techniques, and found that our genetic EM algorithm achieves better clustering structures. Key-Words: Clustering, Gaussian mixture model, EM algorithm, Genetic algorithm, Clustering validity