# Probabilistic Multilevel Clustering via Composite Transportation Distance

arXiv: https://arxiv.org/abs/1810.11911 · HTML: https://mlsanity.com/paper/1810.11911/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [Entropic Gromov-Wasserstein between Gaussian Distributions](https://mlsanity.com/paper/2108.10961/) (2021)
- [Variational Wasserstein Barycenters with c-Cyclical Monotonicity](https://mlsanity.com/paper/2110.11707/) (2021)
- [An Efficient and Effective Evaluator for Text2SQL Models on Unseen and Unlabeled Data](https://mlsanity.com/paper/2603.07841/) (2026)
- [Efficient Forecasting of Large Scale Hierarchical Time Series via Multilevel Clustering](https://mlsanity.com/paper/2205.14104/) (2022)

## Abstract (arXiv)

We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilevel datasets. Finally, we present experimental results with both synthetic and real data to demonstrate the efficiency and scalability of the proposed approach.