Variational Wasserstein Barycenters for Geometric Clustering
This work addresses computational challenges in optimal transport for clustering, but appears incremental as it builds on existing Wasserstein barycenter and Monge map concepts.
The authors tackled the problem of computing Wasserstein barycenters by solving for Monge maps using a variational principle, and demonstrated their application to clustering-related problems such as regularized K-means and Wasserstein barycenter compression, though no concrete numerical results were provided.
We propose to compute Wasserstein barycenters (WBs) by solving for Monge maps with variational principle. We discuss the metric properties of WBs and explore their connections, especially the connections of Monge WBs, to K-means clustering and co-clustering. We also discuss the feasibility of Monge WBs on unbalanced measures and spherical domains. We propose two new problems -- regularized K-means and Wasserstein barycenter compression. We demonstrate the use of VWBs in solving these clustering-related problems.