Distribution Free Decomposition of Multivariate Data

Abstract

We present a practical approach to nonparametric cluster analysis of large data sets. The number of clusters and the cluster centres are automatically derived by mode seeking with the mean shift procedure on a reduced set of points randomly selected from the data. The cluster boundaries are delineated using a k-nearest neighbour technique. The proposed algorithm is stable and efficient, a 10,000 point data set being decomposed in only a few seconds. Complex clustering examples and applications are discussed, and convergence of the gradient ascent mean shift procedure is demonstrated for arbitrary distribution and cardinality of the data.