Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics andâ€¦ (More)

Many applications in data analysis begin with a set of points in a Euclidean space that is partitioned into clusters. Common tasks then are to devise a classifier deciding which of the clusters a newâ€¦ (More)

We prove polynomial-time solvability of a large class of clustering problems where a weighted set of items has to be partitioned into clusters with respect to some balancing constraints. The dataâ€¦ (More)

The study of the diameter of the graph of polyhedra is a classical problem in the theory of linear programming. While transportation polytopes are at the core of operations research and statistics itâ€¦ (More)

The classical k-means algorithm for paritioning n points in Rd into k subsets is one of the most popular and widely spread clustering methods in scientific and business applications. The presentâ€¦ (More)