A clustering method based on the \(L_ 1\)-norm (Q578809)

\textit{G. H. Ball} and \textit{D. J. Hall} [A clustering technique for summarizing multivariate data. Behavioral Science 12, 153-165 (1967)] developed the ISODATA clustering method based on Euclidean distance. In this paper a version of the ISODATA method based on the \(L_ 1\)-norm is given. It is proved that the optimal location parameter vectors for each class of observations are median vectors. An iterative algorithm to obtain the classification of observations and the optimal location parameter vectors is given. The results of Monte Carlo studies of the performance of this method for bivariate normal and bivariate Laplace distributions are presented. Some comparisons of this method and the classical ISODATA method are made.