  In recent years, recurrent quantification analysis (RQA) and its
multi-dimensional version (MdRQA) have emerged as a popular tool for assessing
interpersonal behavioral or physiological synchrony in groups of two or more
individuals. While experimental data in such studies are typically collected
for a fixed, pre-determined duration, naturally occurring phenomena may often
reach a state of transition after an unpredictable or varying duration of time.
The resulting recurrence plots (RPs) across samples cannot be compared directly
via linear scaling because the sensitivity of RQA variables to local dynamics
would vary. We propose to address this by using the sliding window technique on
individual RPs and using the summary statistics of the different RQA variable
distributions computed across the sliding windows to differentiate the dynamics
of the original time series of unequal durations. We first tested our approach
in two simulated models: 1) the Rossler attractor and 2) the Kuramoto model. We
compared the ability of different summary statistics of RQA variable
distributions to accurately predict the dynamic states of the system across
varying levels of noise, unequal lengths of time series, and, in the case of
the Kuramoto model, different numbers of oscillators across samples. We found
that the mode was the most robust to the degree of noise in the signals. We
further tested and validated it on open access data from a recent study
comparing spontaneously generated interpersonal movement synchrony in a dyad.
To our knowledge, this is the first systematic attempt to validate the use of
MdRQA in computing and comparing synchrony between systems of non-uniform
composition and unequal time series data, paving the way for future work that
examines interpersonal synchrony in more naturalistic, ecologically valid
contexts.
