A non-parametric and scale-independent method for cluster analysis - I. The univariate case

Abstract

The detection and analysis of structure and substructure in systemsof galaxies is a well-known problem. Several methods of analysisexist with different ranges of applicability and giving differentresults. The aim of the present paper is to describe a general procedureof wide applicability that is based on a minimum number of generalassumptions and gives an objective, testable, scale-independent andnon-parametric estimate of the clustering pattern of a sample ofobservational data. The method follows the idea that the presenceof a cluster in a data sample is indicated by a peak in the probabilitydensity underlying the data. There are two steps: the first is estimationof the probability density and the second is identification of theclusters. This method allows us to estimate the list of clustersand eventually the fist of isolated objects. Moreover, it gives anestimate of the significance of each cluster and the membership probabilityof each cluster member. Estimates of the presence of possible interloperswithin clusters and of the mutual overlapping of different clustersare also given. In the present work the univariate version of themethod is presented and applied to several examples in order to comparethe results with earlier work. A more general multivariate versionof the method, following the same conceptual path, is in preparation.