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High-dimensional, large-sample astrophysical databases of galaxy clusters,such as the Chandra Deep Field South COMBO-17 database, provide measurements onmany variables for thousands of galaxies and a range of redshifts. Currentunderstanding of galaxy formation and evolution rests sensitively onrelationships between different astrophysical variables; hence an ability todetect and verify associations or correlations between variables is importantin astrophysical research. In this paper, we apply a recently definedstatistical measure called the distance correlation coefficient which can beused to identify new associations and correlations between astrophysicalvariables. The distance correlation coefficient applies to variables of anydimension; it can be used to determine smaller sets of variables that provideequivalent astrophysical information; it is zero only when variables areindependent; and it is capable of detecting nonlinear associations that areundetectable by the classical Pearson correlation coefficient. Hence, thedistance correlation coefficient provides more information than the Pearsoncoefficient. We analyze numerous pairs of variables in the COMBO-17 databasewith the distance correlation method and with the maximal informationcoefficient. We show that the Pearson coefficient can be estimated with higheraccuracy from the corresponding distance correlation coefficient than from themaximal information coefficient. For given values of the Pearson coefficient,the distance correlation method has a greater ability than the maximalinformation coefficient to resolve astrophysical data into highly concentratedV-shapes, which enhances classification and pattern identification. Theseresults are observed over a range of redshifts beyond the local universe andfor galaxies from elliptical to spiral.

Distance Correlation Methods for Discovering Associations in Large Astrophysical Databases