Clustering via nonparametric density estimation

Although Hartigan (1975) had already put forward the idea of connecting identification of subpopulations with regions with high density of the underlying probability distribution, the actual development of methods for cluster analysis has largely shifted towards other directions, for computational convenience. Current computational resources allow us to reconsider this formulation and to develop clustering techniques directly in order to identify local modes of the density. Given a set of observations, a nonparametric estimate of the underlying density function is constructed, and subsets of points with high density are formed through suitable manipulation of the associated Delaunay triangulation. The method is illustrated with some numerical examples.