Optimal Copula Transport for Clustering Multivariate Time Series

TL;DR

This paper introduces a novel clustering method for multivariate time series using optimal transport between copulas, capturing intra- and inter-dependence with robustness to noise and customizable dependency targeting.

Contribution

It proposes a new methodology leveraging optimal copula transport to define dependence-based distances for clustering multivariate time series.

Findings

Effective in capturing complex dependencies.

Robust to noise and deterministic.

Allows targeted dependence analysis.

Abstract

This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence between two time series. Then, optimal copula transport allows us to define two distances between multivariate time series: (i) one for measuring intra-dependence dissimilarity, (ii) another one for measuring inter-dependence dissimilarity based on a new multivariate dependence coefficient which is robust to noise, deterministic, and which can target specified dependencies.