# Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study

arXiv: https://arxiv.org/abs/2510.19306 · HTML: https://mlsanity.com/paper/2510.19306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [The choice of scaling technique matters for classification performance](https://mlsanity.com/paper/2212.12343/) (2022)
- [Comparing the Pearson and Spearman Correlation Coefficients Across Distributions and Sample Sizes: A Tutorial Using Simulations and Empirical Data](https://mlsanity.com/paper/2408.15979/) (2024)
- [On Clustering Time Series Using Euclidean Distance and Pearson Correlation](https://mlsanity.com/paper/1601.02213/) (2016)
- [Stability and Machine Learning Applications of Persistent Homology Using the Delaunay-Rips Complex](https://mlsanity.com/paper/2303.01501/) (2023)
- [Fast Topological Clustering with Wasserstein Distance](https://mlsanity.com/paper/2112.00101/) (2021)
- [Topological Data Analysis for Multivariate Time Series Data](https://mlsanity.com/paper/2204.13799/) (2022)
- [The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series](https://mlsanity.com/paper/2506.19759/) (2025)

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

- [The Shape of Data: Topology Meets Analytics. A Practical Introduction to Topological Analytics and the Stability Index (TSI) in Business](https://mlsanity.com/paper/2511.13503/) (2025)

## Abstract (arXiv)

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, (k)-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.