Interpoint distances: Applications, properties, and visualization

This article surveys recent development on Euclidean interpoint distances (IPDs). IPDs find applications in many scientific fields and are the building blocks of several multivariate techniques such as comparison of distributions, clustering, classification, and multidimensional scaling. In this article, we explore IPDs, discuss their properties and applications, and present their distributions for several families, including the multivariate normal, multivariate Bernoulli, multivariate power series, and the unified hypergeometric distributions. We consider two groups of observations in Rd and present a simultaneous plot of the empirical cumulative distribution functions of the within and between IPDs to visualize and examine the equality of the underlying distribution functions of the observations.