# Fast Topological Clustering with Wasserstein Distance

arXiv: https://arxiv.org/abs/2112.00101 · HTML: https://mlsanity.com/paper/2112.00101/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 63 references that are in the map.
- First posted on arXiv 30 Nov 2021.

## Builds on (most cited first, 16 of 16)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport](https://mlsanity.com/paper/1805.08331/) (2018)
- [Continuous Regularized Wasserstein Barycenters](https://mlsanity.com/paper/2008.12534/) (2020)
- [Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support](https://mlsanity.com/paper/1510.00012/) (2015)
- [When OT meets MoM: Robust estimation of Wasserstein Distance](https://mlsanity.com/paper/2006.10325/) (2020)
- [Progressive Wasserstein Barycenters of Persistence Diagrams](https://mlsanity.com/paper/1907.04565/) (2019)
- [Variational Wasserstein Clustering](https://mlsanity.com/paper/1806.09045/) (2018)
- [Topological Learning for Brain Networks](https://mlsanity.com/paper/2012.00675/) (2020)

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

- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Functional connectomes of neural networks](https://mlsanity.com/paper/2412.15279/) (2024)
- [Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study](https://mlsanity.com/paper/2510.19306/) (2025)
- [Topological Continual Learning with Wasserstein Distance and Barycenter](https://mlsanity.com/paper/2210.02661/) (2022)
- [Hierarchical topological clustering](https://mlsanity.com/paper/2601.00892/) (2025)

## Abstract (arXiv)

The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and dense networks whose node degrees range over multiple orders of magnitude. In this paper, we propose a novel and computationally practical topological clustering method that clusters complex networks with intricate topology using principled theory from persistent homology and optimal transport. Such networks are aggregated into clusters through a centroid-based clustering strategy based on both their topological and geometric structure, preserving correspondence between nodes in different networks. The notions of topological proximity and centroid are characterized using a novel and efficient approach to computation of the Wasserstein distance and barycenter for persistence barcodes associated with connected components and cycles. The proposed method is demonstrated to be effective using both simulated networks and measured functional brain networks.