Valeriepieris Circles for Spatial Data Analysis

Abstract

The Valeriepieris (VP) circle is the smallest circle containing half of the world's population. The Valeriepieris circle acts as a spatial median, splitting spatial data into two halves in a unique way. In this article the idea of the VP circle is generalized and a fast algorithm to compute it is described. This algorithm has been implemented in Python and is available for download and use. The VP circle is compared to other measures of center 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 behavior. Finally a measure of population “centralization” is constructed which measures the tendency of a territory to be dominated by a single population center or to have a more even distribution of population. Thus, VP circles unify measures of population center, dispersion and centralization while also being useful for more detailed modeling efforts.