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DISTANCE CORRELATION METHODS FOR DISCOVERING ASSOCIATIONS IN LARGE ASTROPHYSICAL DATABASES

Authors :
Mercedes T. Richards
Donald St. P. Richards
E. Martínez-Gómez
Source :
The Astrophysical Journal. 781:39
Publication Year :
2014
Publisher :
American Astronomical Society, 2014.

Abstract

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; it can be used to determine smaller sets of variables that provide equivalent astrophysical information; it is zero only when variables are independent; and it 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 Pearson coefficient, the distance correlation method has a greater ability than the maximal information coefficient to resolve astrophysical data into highly concentrated 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.<br />Comment: 11 pages, 6 figures, 4 tables; Astrophysical Journal, accepted, in press

Details

ISSN :
15384357 and 0004637X
Volume :
781
Database :
OpenAIRE
Journal :
The Astrophysical Journal
Accession number :
edsair.doi.dedup.....ec008f6980ef5b0b7db9d3492c413392
Full Text :
https://doi.org/10.1088/0004-637x/781/1/39