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Journal Article

Graph database solution for higher-order spatial statistics in the era of big data


Hoyle,  B.
Optical and Interpretative Astronomy, MPI for Extraterrestrial Physics, Max Planck Society;

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Sabiu, C. G., Hoyle, B., Kim, J., & Li, X.-D. (2019). Graph database solution for higher-order spatial statistics in the era of big data. The Astrophysical Journal Supplement Series, 242(2): 29. doi:10.3847/1538-4365/ab22b5.

Cite as: http://hdl.handle.net/21.11116/0000-0004-800F-B
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 Rn . 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 ~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.