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Entropy 2012, 14(5), 865-879; doi:10.3390/e14050865
Article

Entropic Approach to Multiscale Clustering Analysis

1,*  and 2
1 School of Computer Science, University of Birmingham, Edgbaston B15 2TT Birmingham, UK 2 Dipartimento di Fisica e Astronomia, Universitá di Catania and INFN, Via S. Sofia 64, 95123 Catania, Italy
* Author to whom correspondence should be addressed.
Received: 20 February 2012 / Revised: 3 May 2012 / Accepted: 4 May 2012 / Published: 9 May 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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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.
Keywords: Kullback–Leibler divergence; multiscale clustering; ultra-high energy cosmic rays; extreme value theory Kullback–Leibler divergence; multiscale clustering; ultra-high energy cosmic rays; extreme value theory
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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De Domenico, M.; Insolia, A. Entropic Approach to Multiscale Clustering Analysis. Entropy 2012, 14, 865-879.

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