Entropic Approach to Multiscale Clustering Analysis

Abstract

Recently, a novel method has been introduced to estimate the statistical significance of clustering in the direction distribution of objects. The method involves a multiscale procedure, based on the Kullback-Leibler divergence and the Gumbel statistics of extreme values, providing high discrimination power, even in presence of strong background isotropic contamination. It is shown that the method is: (i) semi-analytical, drastically reducing computation time; (ii) very sensitive to small, medium and large scale clustering; (iii) not biased against the null hypothesis. Applications to the physics of ultra-high energy cosmic rays, as a cosmological probe, are presented and discussed. © 2012 by the authors.