The Use of Domination Number of a Random Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association

TL;DR

This paper introduces a new proximity map and digraph in higher dimensions to analyze the domination number, providing a method for testing spatial patterns like segregation and association.

Contribution

It develops an asymptotic distribution for the domination number of the new digraph, enabling advanced spatial pattern testing in multi-dimensional data.

Findings

Asymptotic distribution of domination number derived

Effective testing for segregation and association patterns

Extension of proximity catch digraphs to higher dimensions

Abstract

Priebe et al. (2001) introduced the class cover catch digraphs and computed the distribution of the domination number of such digraphs for one dimensional data. In higher dimensions these calculations are extremely difficult due to the geometry of the proximity regions; and only upper-bounds are available. In this article, we introduce a new type of data-random proximity map and the associated (di)graph in $\mathbb R^d$. We find the asymptotic distribution of the domination number and use it for testing spatial point patterns of segregation and association.