MulGuisin, a Topological Network Finder and its Performance on Galaxy Clustering

We introduce a new clustering algorithm, MulGuisin (MGS), that can identify distinct galaxy over-densities using topological information from the galaxy distribution. This algorithm was first introduced in an LHC experiment as a Jet Finder software, which looks for particles that clump together in close proximity. The algorithm preferentially considers particles with high energies and merges them only when they are closer than a certain distance to create a jet. MGS shares some similarities with the minimum spanning tree (MST) since it provides both clustering and network-based topology information. Also, similar to the density-based spatial clustering of applications with noise (DBSCAN), MGS uses the ranking or the local density of each particle to construct clustering. In this paper, we compare the performances of clustering algorithms using controlled data and some realistic simulation data as well as the SDSS observation data, and we demonstrate that our new algorithm find networks most efficiently and it defines galaxy networks in a way that most closely resembles human vision.Comment: 15 pages,12 figure

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 $<r_{max}$. Through bench-marking we show the computational advantage of our new graph based algorithm over more traditional methods. We show that all 3-point configurations up to and beyond the 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 $0.43<z<0.7$.Comment: 9 pages, 8 figures, submitte