Deriving Cluster Analytic Distance Functions from Gaussian Mixture Models

The reliable detection of clusters in datasets of non-trivial dimensionality is notoriously difficult. Clustering algorithms are generally driven by some distance function (usually Euclidean) defined over pairs of examples, which implicitly treats distances within and between clusters alike. In this paper, a more effective distance measure is proposed, derived from an a priori estimated Gaussian mixture model. Examples illustrate how the proposed approach can effectively de-emphasise within-cluster structure, and thus implicitly magnify the separation between regions of high data density.