Optimal Copula Transport for Clustering Multivariate Time Series
This addresses the problem of clustering multivariate time series for researchers and practitioners in fields like finance or healthcare, but it appears incremental as it builds on existing copula and optimal transport techniques.
The paper tackles clustering multivariate time series by introducing a method based on optimal transport between copulas, which defines distances for intra- and inter-dependence dissimilarity, resulting in a robust and deterministic multivariate dependence coefficient.
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.