Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed. Abstract: Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed. Keywords

A new method is proposed to generate sample Gaussian mixture distributions according to pre-specified overlap characteristics. Such methodology is useful in the context of evaluating performance of clustering algorithms. Our suggested approach involves derivation of and calculation of the exact overlap between every cluster pair, measured in terms of their total probability of misclassification, and then guided simulation of Gaussian components satisfying pre-specified overlap characteristics. The algorithm is illustrated in two and five dimensions using contour plots and parallel distribution plots, respectively, which we introduce and develop to display mixture distributions in higher dimensions. We also study properties of the algorithm and variability in the simulated mixtures. The utility of the suggested algorithm is demonstrated via a study of initialization strategies in Gaussian clustering.

The R package MixSim is a new tool that allows simulating mixtures of Gaussian distributions with different levels of overlap between mixture components. Pairwise overlap, defined as a sum of two misclassification probabilities, measures the degree of interaction between components and can be readily employed to control the clustering complexity of datasets simulated from mixtures. These datasets can then be used for systematic performance investigation of clustering and finite mixture modeling algorithms. Among other capabilities of MixSim, there are computing the exact overlap for Gaussian mixtures, simulating Gaussian and non-Gaussian data, simulating outliers and noise variables, calculating various measures of agreement between two partitionings, and constructing parallel distribution plots for the graphical display of finite mixture models. All features of the package are illustrated in great detail. The utility of the package is highlighted through a small comparison study of several popular clustering algorithms.

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