Analysis of UN Voting Patterns via Diffusion Geometry and Thematic Clustering

We apply a range of data mining techniques to analyze voting patterns in the United Nations. We begin with non-linear dimensionality reduction, showing that diffusion geometry reveals an historically relevant organization of countries based on their UN voting patterns. Key historical events can be ``read out'' from these embeddings, such as de Gaulle's influence on France and the breakup of the Soviet Union. These events are not apparent in other (e.g., PCA) embeddings. We then switch to an organization of resolutions, revealing dominant themes during different political epochs. Formally themes are introduced as summaries (eigenfunctions) within a modified hierarchical clustering algorithm.