# Exploring and measuring non-linear correlations: Copulas, Lightspeed Transportation and Clustering

arXiv: https://arxiv.org/abs/1610.09659 · HTML: https://mlsanity.com/paper/1610.09659/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2016.

## Built on by (most cited first, 2 of 2)

- [Lead-lag detection and network clustering for multivariate time series with an application to the US equity market](https://mlsanity.com/paper/2201.08283/) (2022)
- [Deep into The Domain Shift: Transfer Learning through Dependence Regularization](https://mlsanity.com/paper/2305.19499/) (2023)

## Abstract (arXiv)

We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for providing a relevant geometry to the copulas, and clustering for summarizing the main dependence patterns found between the variables. Some of the clusters centers can be used to parameterize a novel dependence coefficient which can target or forget specific dependence patterns. Finally, we illustrate and benchmark the methodology on several datasets. Code and numerical experiments are available online for reproducible research.