Estimating and Controlling Overlap in Gaussian Mixtures for Clustering Methods Evaluation

The ad hoc nature of the clustering methods makes simulated data paramount in assessing the performance of clustering methods. Real datasets could be used in the evaluation of clustering methods with the major drawback of missing the assessment of many test scenarios. In this paper, we propose a formal quantification of component overlap. This quantification is derived from a set of theorems which allow us to derive an automatic method for artificial data generation. We also derive a method to estimate parameters of existing models and to evaluate the results of other approaches. Automatic estimation of the overlap rate can also be used as an unsupervised learning approach in data mining to determine the parameters of mixture models from actual observations.