A Measurement of Overlap Rate Between Gaussiancomponents

Overlapping clusters often appear in cluster analysis in the data mining. However, the phenomenon of cluster overlapping is still not mathematically well characterized, especially in multivariate cases. In this paper, we are interested in the overlap phenomenon between Gaussian clusters, since the Gaussian mixture is a fundamental data distribution model suitable for many clustering algorithms. We introduce the novel concept of the ridge curve and establish a theory on the degree of overlap between two components. Based on this theory, we develop an algorithm for calculating the overlap rate. We investigate factors that affect the value of the overlap rate, and show how the theory can be used to generate "truthed data" as well as to measure the overlap rate between a given pair of clusters or components in a mixture.