# Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes

arXiv: https://arxiv.org/abs/1910.04483 · HTML: https://mlsanity.com/paper/1910.04483/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Fixed Support Tree-Sliced Wasserstein Barycenter](https://mlsanity.com/paper/2109.03431/) (2021)
- [Iterative Alignment Flows](https://mlsanity.com/paper/2104.07232/) (2021)
- [Learning Ultrametric Trees for Optimal Transport Regression](https://mlsanity.com/paper/2210.12288/) (2022)

## Abstract (arXiv)

We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance. Drawing on the tree structure, we propose an efficient algorithmic approach to solve the tree-Wasserstein barycenter and its variants. The proposed approach is not only fast for computation but also efficient for memory usage. Exploiting the tree-Wasserstein barycenter and its variants, we scale up multi-level clustering and scalable Bayes, especially for large-scale applications where the number of supports in probability measures is large. Empirically, we test our proposed approach against other baselines on large-scale synthetic and real datasets.