Optimal Copula Transport for Clustering Multivariate Time Series

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.