# On Efficient Multilevel Clustering via Wasserstein Distances

arXiv: https://arxiv.org/abs/1909.08787 · HTML: https://mlsanity.com/paper/1909.08787/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2019.

## Built on by (most cited first, 5 of 5)

- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexity](https://mlsanity.com/paper/2108.07992/) (2021)
- [An Efficient and Effective Evaluator for Text2SQL Models on Unseen and Unlabeled Data](https://mlsanity.com/paper/2603.07841/) (2026)
- [Keypoint-Guided Optimal Transport: Models, Algorithms, and Applications](https://mlsanity.com/paper/2303.13102/) (2023)
- [The geometry of financial institutions -- Wasserstein clustering of financial data](https://mlsanity.com/paper/2305.03565/) (2023)

## Abstract (arXiv)

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose several variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experimental results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.