ABSTRACT
A cluster should comprise points that diffuse from a mode, and experience gained working on real problems. The cluster is only believable if it is a component within a finite mixture model. In many cases, being appropriate in light of the data will mean that each component has convex contours so that each cluster is convex. Complete external isolation will not be possible in many real analyses; however, the idea of internal cohesion seems quite compatible with the idea of a cluster corresponding to a unimodal component in an appropriate finite mixture. For quite some time, there has been support for the model-based approach to clustering. If one accepts the definition of a cluster, then it makes sense to use mixture model-based approaches for clustering and, by extension, for classification. Steinley and Brusco discuss the performance of k-means clustering versus Gaussian model-based clustering and argue that the former approach might be preferable in some circumstances.
