A non-parametric and scale-independent method for cluster analysis II: the multivariate case

A general method is described for detecting and analysing galaxy systems. The multivariate geometrical structure of the sample is studied by using an extension of the method which we introduced in a previous paper. The method is based on an estimate of the probability density underlying a data sample. The density is estimated by using an iterative and adaptive kernel estimator. The used kernels have spherical symmetry, however we describe a method in order to estimate the locally optimal shape of the kernels. We use the results of the geometrical structure analysis in order to study the effects that is has on the cluster parameter estimate. This suggests a possible way to distinguish between structure and substructure within a sample. The method is tested by using simulated numerical models and applied to two galaxy samples taken from the literature. The results obtained for the Coma cluster suggest a core-halo structure formed by a large number of geometrically independent systems. A different conclusion is suggested by the results for the Cancer cluster indicating the presence of at least two independent structures both containing substructure. The dynamical consequences of the results obtained from the geometrical analysis will be described in a later paper. Further applications of the method are suggested and are currently in progress.