Graph Database Solution for Higher-order Spatial Statistics in the Era of Big Data

摘要

We present an algorithm for the fast computation of the general N-point spatial correlation functions of any discrete point set embedded within an Euclidean space of R-n. Utilizing the concepts of kd-trees and graph databases, we describe how to count all possible N-tuples in binned configurations within a given length scale, e.g., all pairs of points or all triplets of points with side lengths < r(MAX). Through benchmarking, we show the computational advantage of our new graph-based algorithm over more traditional methods. We show measurements of the three-point correlation function up to scales of similar to 200 Mpc (beyond the baryon acoustic oscillation scale in physical units) using current Sloan Digital Sky Survey (SDSS) data. Finally, we present a preliminary exploration of the small-scale four-point correlation function of 568,776 SDSS Constant (stellar) Mass (CMASS) galaxies in the northern Galactic cap over the redshift range of 0.43 < z < 0.7. We present the publicly available code GRAMSCI (GRAph Made Statistics for Cosmological Information; bitbucket.org/csabiu /gramsci), under a Gnu is Not Unix (GNU) General Public License.