  We propose a new clustering method based on optimal transportation. We solve
optimal transportation with variational principles, and investigate the use of
power diagrams as transportation plans for aggregating arbitrary domains into a
fixed number of clusters. We iteratively drive centroids through target domains
while maintaining the minimum clustering energy by adjusting the power
diagrams. Thus, we simultaneously pursue clustering and the Wasserstein
distances between the centroids and the target domains, resulting in a
measure-preserving mapping. We demonstrate the use of our method in domain
adaptation, remeshing, and representation learning on synthetic and real data.
