Multivariate Joint Recurrence Quantification Analysis: detecting coupling between time series of different dimensionalities

Abstract

One challenge with the analysis of complex systems and the interaction between such systems is that they are composed of different numbers of components, or simply the fact that a different number of observables is available for each system. The challenge is how to analyze the interaction of two systems which are not described by the same number of variables. Here, we present multivariate joint recurrence quantification analysis (MvJRQA), a recurrence-based technique that allows to analyze coupling properties between multivariate datasets that differ in dimensionality (i.e., number of observables) and type of data (such as nominal or interval-scaled, for example). First, we introduce the methods, and test it on simulated data from linear and nonlinear systems. Then we apply it to an empirical dataset of EEG and eye tracking data. We introduce the joint recurrence coupling indicator (JRCI) as a measure to assess and compare coupling between systems. Finally, we discuss practical issues regarding the application of the method.