Multidimensional Recurrence Quantification Analysis (MdRQA) for the Analysis of Multidimensional Time-Series: A Software Implementation in MATLAB and Its Application to Group-Level Data in Joint Action

Abstract

We introduce Multidimensional Recurrence Quantification Analysis (MdRQA) as a tool to analyze multidimensional time-series data. We show how MdRQA can be used to capture the dynamics of high-dimensional signals, and how MdRQA can be used to assess coupling between two or more variables. In particular, we describe applications of the method in research on joint and collective action, as it provides a coherent analysis framework to systematically investigate dynamics at different group levels—from individual dynamics, to dyadic dynamics, up to global group-level of arbitrary size. The Appendix in Supplementary Material contains a software implementation in MATLAB to calculate MdRQA measures.

Beyond Dyadic Coordination: Multimodal Behavioral Irregularity in Triads Predicts Facets of Collaborative Problem Solving

“…We used each participant's (PA, PB, and PC) speech rate (SR), body movement (BM), as well as UI‐Minecraft change and UI‐code change 1 Hz time series to conduct an eight‐dimensional (SR PA , SR PB, SR PC, BM PA , BM PB , BM PC, UI‐Minecraft, UI‐Code) MdRQA for each team using code adapted from Wallot et al (). Each time series was z ‐scored per time series prior to analysis so the different dimensions were on equal footing.…”

Beyond Synchrony: Joint Action in a Complex Production Task Reveals Beneficial Effects of Decreased Interpersonal Synchrony

“…MdRQA is a time series analysis technique that measures the relationship between two or more time series and can be used to quantify their degree of synchrony [27]. MdRQA was inspired by work of Thomasson and colleagues [28], who were the first to use recurrence analysis of the Euclidean distance of a multivariate signal (EEG channels) to quantify the synchronization of multivariate brain activity.…”

“…MdRQA was inspired by work of Thomasson and colleagues [28], who were the first to use recurrence analysis of the Euclidean distance of a multivariate signal (EEG channels) to quantify the synchronization of multivariate brain activity. MdRQA [27] is an extension of cross-recurrence analysis, which is a nonlinear correlation analysis that quantifies the evolution of two time series [29]; it is a prominent technique for the analysis of temporal coordination and has been used in a variety of joint action studies [6,19,26,30,31]. To conduct recurrence analysis, the time series are projected into a phase space by the method of time-delayed embedding.…”

“…We chose MdRQA to compute measures of synchrony because it allowed us to integrate information from multiple (i.e., more than two) time series [27], and would also capture temporal correlations between time series that do not exhibit well-defined phases (such as rocking in rocking chairs [11]), which was the case with our data—see Fig 4 for examples of hand acceleration and heart rate time series, as well as their associated recurrence plots. Moreover, bivariate scatter plots of the majority of pairs of signals did not conform to a linear (or curve-linear) relationship.…”

“…We are merely interested in using RQA as a correlational method that quantifies the correlational strength of a relationship between multiple signals for the reasons provided. For a detailed description of MdRQA and MATLAB code to run the analysis, see [27]. …”