# Automated regime classification in multidimensional time series data using sliced Wasserstein k-means clustering

arXiv: https://arxiv.org/abs/2310.01285 · HTML: https://mlsanity.com/paper/2310.01285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 6 of 6)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [On the Wasserstein median of probability measures](https://mlsanity.com/paper/2209.03318/) (2022)
- [Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures](https://mlsanity.com/paper/2306.15835/) (2023)

## Abstract (arXiv)

Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to classify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in detail the behaviour of the Wasserstein k-means clustering algorithm applied to synthetic one-dimensional time series data. We extend the previous work by studying, in detail, the dynamics of the clustering algorithm and how varying the hyperparameters impacts the performance over different random initialisations. We compute simple metrics that we find to be useful in identifying high-quality clusterings. We then extend the technique of Wasserstein k-means clustering to multidimensional time series data by approximating the multidimensional Wasserstein distance as a sliced Wasserstein distance, resulting in a method we call 'sliced Wasserstein k-means (sWk-means) clustering'. We apply the sWk-means clustering method to the problem of automated regime classification in multidimensional time series data, using synthetic data to demonstrate the validity and effectiveness of the approach. Finally, we show that the sWk-means method is able to identify distinct market regimes in real multidimensional financial time series, using publicly available foreign exchange spot rate data as a case study. We conclude with remarks about some limitations of our approach and potential complementary or alternative approaches.