In 1983, A. Hardy proposed a new k-clustering procedure based on the thoery of Poisson processes. The hypervolume cirterion, deduced from the statistical model by the method of maximum likelihood estimation, consists in minimizing the sum of the Lebesgue measures of the convex hulls of the k clusters. It was assumed that the clusters are convex. k was supposed fixed. The purpose of this paper is to propose some statistical tests based on the hypervolume clustering method to detect a structure in a data set and to determine the numer of natural clusters. The first one is based on the estimation of a convex set; the second one is a likelihood ratio test. The paper shows the results obtained on various data sets.
