Comparison of Cross-Correlation and Joint-Recurrence Quantification Analysis Based Methods for Estimating Coupling Strength in Non-linear Systems - Tolston, Michael T.; Funke, Gregory J.; Shockley, Kevin (Frontiers in Applied Mathematics and Statistics, 2020)
Time-delay stability (TDS) analysis is a method for quantifying interactions in multivariate systems by identifying stable temporal relationships in time series data (1). This method has been used to create network representations of complex systems. As originally presented, the TDS method relies on cross-correlation—a linear analysis that is restricted to estimating relationships between unidimensional time series, and which, by itself, often does not adequately characterize interactions between many nonlinear complex systems of theoretical and practical interest. Thus, modifying TDS so that it relies on joint recurrence quantification analysis (JRQA), an intrinsically nonlinear multidimensional framework, and then comparing the ability of the two approaches to detect interactions in nonlinear systems is an important task. In the present work, we first show how TDS can be extended using JRQA, a method which is capable of multidimensional assessment of relationships in nonlinear systems. In our application of JRQA, we introduce a modification in the form of a weighting factor that accounts for the truncation of time series that results from time-delayed JRQA. We also modify TDS by correcting for a bias in the method, and show how analogs of recurrence-based metrics can also be obtained for TDS. We evaluate how TDS results obtained with JRQA compare to those obtained with cross-correlation for known dynamics of coupled non-linear oscillators and from unknown dynamics of multivariate behavioral signals measured from dyads performing a joint problem-solving task. We conclude that TDS using cross-correlation provides results that are comparable to those obtained with JRQA at a much-reduced computational cost.