Edge detecting new physics the Voronoi way

Abstract

Edge detection is an important tool in the search for and exploration of physics beyond the standard model. Ideally one would be able to perform edge detection in a relatively model-independent way, however most analyses rely on more detailed properties (i.e. “shapes” or likelihood distributions) of the variable(s) of interest. We therefore present a sketch of how edge detection can be accomplished using Voronoi tessellations, focusing on the case of two-dimensional distributions for simplicity. After deriving some useful properties of the Voronoi tessellations of simplified distributions containing edges, we propose several algorithms for tagging the Voronoi cells in the vicinity of kinematic edges in real data and show that the efficiency of our methods is improved by the addition of a few Voronoi relaxation steps via Lloyd's method. Our results suggest specifically that Voronoi-based methods should be useful for relatively model-independent edge detection, and, more generally, that the wider adaptation of Voronoi tessellations may be useful in collider physics.