Variational Wasserstein Clustering

Liang Mi, Wen Zhang, Xianfeng Gu, Yalin Wang

Abstract

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

Figures (click on each for a larger version):

Image of Variational Wasserstein Clustering
Image of Variational Wasserstein Clustering
Image of Variational Wasserstein Clustering
Image of Variational Wasserstein Clustering
Image of Variational Wasserstein Clustering
Image of Variational Wasserstein Clustering

Related Publications