Variational Wasserstein Clustering
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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 centroids and target domains, resulting in a robust measure-preserving mapping. In general, there are two approaches for solving optimal transportation problem -- Kantorovich's v.s. Brenier's. While most researchers focus on Kantorovich's approach, we propose a solution to clustering problem following Brenier's approach and achieve a competitive result with the state-of-the-art method. We demonstrate our applications to different areas such as domain adaptation, remeshing, and representation learning on synthetic and real data.
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