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

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 $\mathbb{R}^n$. 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 $Baryon Acoustic Oscillation scale ($\sim$200 Mpc in physical units) can be performed on current SDSS data in reasonable time. Finally we present the first measurements of the 4-point correlation function of $\sim$0.5 million SDSS galaxies over the redshift range $0.43

Keywords:

• Length scale
• Discrete mathematics
• Spatial analysis
• Astronomy
• Spatial correlation
• Correlation function
• Euclidean space
• Graph database
• Baryon
• Physics
• Redshift
• Astrophysics
• Computation

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