Clustering spatial data through optimal transport

This paper introduces a strategy for clustering point clouds generated by a spatial point process. The input dataset is a set of points in Rd describing several events, each one made by a subset of the dataset. Our aim is to discover groups of similar events by means of an appropriate clustering strategy. We propose to cluster the events using a variant of the k-means algorithm based on the Sliced Wasserstein distance for probability measures. Preliminary results show the effectiveness of our proposal.