Valeriepieris Circles for Spatial Data Analysis

TL;DR

This paper introduces the Valeriepieris circle as a novel spatial median for population data, providing a fast algorithm, software, and new insights into population distribution and centralisation.

Contribution

It generalizes the Valeriepieris circle concept, develops a fast algorithm and software, and introduces a new measure of population centralisation.

Findings

VP circle reflects differences between countries and over time

A new representation of population distributions is proposed

A mathematical model of VP circle behaviour is developed

Abstract

The Valeriepieris circle is the smallest circle that can be draw on the globe containing half of the world's population. The Valeriepieris (VP) circle acts as a spatial median, effectively splitting spatial data into two halves in a unique way. In this paper the idea of the VP circle is generalised and a fast algorithm and corresponding software package to compute it are described. The VP circle is compared to other measures of centre and dispersion for population distributions and is shown to reflect expected differences between countries and changes over time. By studying the VP circle as a function of the included population fraction a new way of representing population distributions is constructed, as well as a mathematical model of its expected behaviour. Finally a measure of population `centralisation' is constructed which measures the tendency of a territory to be dominated by a single population centre or to have a more even distribution of population.