Simulating Data to Study Performance of Finite Mixture Modeling and Clustering Algorithms

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.