Condorcet Optimal Clustering with Delaunay Triangulation: Climate Zones and World Happiness Insights

Abstract

Condorcet clustering methods have the attractive features of producing clusterings which place similar points in the same cluster and dissimilar points in different clusters as well as not requiring a priori specification of the number of clusters. They have the disadvantages of being combinatorially hard and the method produces only convex clusters. We propose a novel modification to this method, which improves it significantly on both accounts and works particularly well when applied to social network type data sets. Specifically, we reduce the domain of the clustering to be over a Delaunay triangulation, whose size scales as $O(n^{\lfloor m/2 \rfloor })$ where n is the number of records and m is the number of attributes used for the clustering. The triangulation also limits focus to local structure, which allows for non-convex clusterings. We demonstrate its use in comparison to other well-known heuristic methods using several constructed datasets, then use it to cluster real-world datasets.

This research was completed in partial fulfillment of the United States Military Academy’s Network Science Minor program and sponsored by the West Point Network Science Center.