Objective Criteria for the Evaluation of Clustering Methods

Abstract

Human mobility is known to be distributed across several orders of magnitude\nof physical distances , which makes it generally difficult to endogenously find\nor define typical and meaningful scales. Relevant analyses, from movements to\ngeographical partitions, seem to be relative to some ad-hoc scale, or no scale\nat all. Relying on geotagged data collected from photo-sharing social media, we\napply community detection to movement networks constrained by increasing\npercentiles of the distance distribution. Using a simple parameter-free\ndiscontinuity detection algorithm, we discover clear phase transitions in the\ncommunity partition space. The detection of these phases constitutes the first\nobjective method of characterising endogenous, natural scales of human\nmovement. Our study covers nine regions, ranging from cities to countries of\nvarious sizes and a transnational area. For all regions, the number of natural\nscales is remarkably low (2 or 3). Further, our results hint at scale-related\nbehaviours rather than scale-related users. The partitions of the natural\nscales allow us to draw discrete multi-scale geographical boundaries,\npotentially capable of providing key insights in fields such as epidemiology or\ncultural contagion where the introduction of spatial boundaries is pivotal.\n