Variational Wasserstein Clustering
This method addresses clustering problems in machine learning, offering a novel approach for tasks like domain adaptation, but it appears incremental as it builds on existing optimal transport and variational techniques.
The paper tackles clustering by integrating optimal transport with variational principles, using power diagrams to map data into clusters while preserving Wasserstein distances, and demonstrates applications in domain adaptation, remeshing, and representation learning on synthetic and real data.
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.