# Variational Wasserstein Clustering

arXiv: https://arxiv.org/abs/1806.09045 · HTML: https://mlsanity.com/paper/1806.09045/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2018.

## Built on by (most cited first, 11 of 11)

- [On the Relation between Rectified Flows and Optimal Transport](https://mlsanity.com/paper/2505.19712/) (2025)
- [Online Video Super-Resolution with Convolutional Kernel Bypass Graft](https://mlsanity.com/paper/2208.02470/) (2022)
- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [Learning to Generate Wasserstein Barycenters](https://mlsanity.com/paper/2102.12178/) (2021)
- [Fast Topological Clustering with Wasserstein Distance](https://mlsanity.com/paper/2112.00101/) (2021)
- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest](https://mlsanity.com/paper/2201.00087/) (2022)
- [Analysis of Utterance Embeddings and Clustering Methods Related to Intent Induction for Task-Oriented Dialogue](https://mlsanity.com/paper/2212.02021/) (2022)
- [Estimation of Stationary Optimal Transport Plans](https://mlsanity.com/paper/2107.11858/) (2021)
- [Adjustment of Cluster-Then-Predict Framework for Multiport Scatterer Load Prediction](https://mlsanity.com/paper/2602.08129/) (2026)
- [EMS Coreset: An Efficient Expectation-Maximization Algorithm for Sinkhorn Coreset](https://mlsanity.com/paper/2608.16101/) (2026)

## Abstract (arXiv)

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.