# Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering Multivariate Time Series

arXiv: https://arxiv.org/abs/1604.08634 · HTML: https://mlsanity.com/paper/1604.08634/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2016.

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

- [A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions](https://mlsanity.com/paper/2302.08175/) (2023)

## Abstract (arXiv)

We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account the dependence information while clustering, we need a distance between copulas. In this work, we compare renowned distances between distributions: the Fisher-Rao geodesic distance, related divergences and optimal transport, and discuss their advantages and disadvantages. Applications of such methodology can be found in the clustering of financial assets. A tutorial, experiments and implementation for reproducible research can be found at www.datagrapple.com/Tech.