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Title: Distance correlation methods for discovering associations in large astrophysical databases

High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between different astrophysical variables; hence an ability to detect and verify associations or correlations between variables is important in astrophysical research. In this paper, we apply a recently defined statistical measure called the distance correlation coefficient, which can be used to identify new associations and correlations between astrophysical variables. The distance correlation coefficient applies to variables of any dimension, can be used to determine smaller sets of variables that provide equivalent astrophysical information, is zero only when variables are independent, and is capable of detecting nonlinear associations that are undetectable by the classical Pearson correlation coefficient. Hence, the distance correlation coefficient provides more information than the Pearson coefficient. We analyze numerous pairs of variables in the COMBO-17 database with the distance correlation method and with the maximal information coefficient. We show that the Pearson coefficient can be estimated with higher accuracy from the corresponding distance correlation coefficient than from the maximal information coefficient. For given values of the Pearsonmore » coefficient, the distance correlation method has a greater ability than the maximal information coefficient to resolve astrophysical data into highly concentrated horseshoe- or V-shapes, which enhances classification and pattern identification. These results are observed over a range of redshifts beyond the local universe and for galaxies from elliptical to spiral.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Statistics, Instituto Tecnológico Autónomo de México, Del. Álvaro Obregón, 04510, México D. F. (Mexico)
  2. Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802 (United States)
  3. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, D-69120 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
22348162
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 781; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ASTROPHYSICS; CATALOGS; CLASSIFICATION; CORRELATIONS; DATA; DISTANCE; EVOLUTION; GALAXIES; GALAXY CLUSTERS; NONLINEAR PROBLEMS; RED SHIFT; STATISTICS; UNIVERSE