Variational Wasserstein Barycenters for Geometric Clustering
Machine Learning
2023-03-31 v2 Machine Learning
Abstract
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.
Cite
@article{arxiv.2002.10543,
title = {Variational Wasserstein Barycenters for Geometric Clustering},
author = {Liang Mi},
journal= {arXiv preprint arXiv:2002.10543},
year = {2023}
}