# The geometry of financial institutions -- Wasserstein clustering of financial data

arXiv: https://arxiv.org/abs/2305.03565 · HTML: https://mlsanity.com/paper/2305.03565/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 12 of 12)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Gromov-Wasserstein Alignment of Word Embedding Spaces](https://mlsanity.com/paper/1809.00013/) (2018)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [Wasserstein K-means for clustering probability distributions](https://mlsanity.com/paper/2209.06975/) (2022)
- [k-POD: A Method for k-Means Clustering of Missing Data](https://mlsanity.com/paper/1411.7013/) (2014)
- [Hybrid Wasserstein Distance and Fast Distribution Clustering](https://mlsanity.com/paper/1812.11026/) (2018)
- [On Efficient Multilevel Clustering via Wasserstein Distances](https://mlsanity.com/paper/1909.08787/) (2019)
- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [On clustering uncertain and structured data with Wasserstein barycenters and a geodesic criterion for the number of clusters](https://mlsanity.com/paper/1912.11801/) (2019)

## Built on by (most cited first, 1 of 1)

- [An Agglomerative Clustering of Simulation Output Distributions Using Regularized Wasserstein Distance](https://mlsanity.com/paper/2407.12100/) (2024)

## Abstract (arXiv)

The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative and intelligible map. Financial regulation is a field that exemplifies this need, as regulators require diverse and often highly granular data from financial institutions to monitor and assess their activities. However, processing and analyzing such data can be a daunting task, especially given the challenges of dealing with missing values and identifying clusters based on specific features. To address these challenges, we propose a variant of Lloyd's algorithm that applies to probability distributions and uses generalized Wasserstein barycenters to construct a metric space which represents given data on various objects in condensed form. By applying our method to the financial regulation context, we demonstrate its usefulness in dealing with the specific challenges faced by regulators in this domain. We believe that our approach can also be applied more generally to other fields where large and complex data sets need to be represented in concise form.