  One issue with the analysis of complex systems and the interaction between
such systems is that they are composed of different number 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. The approach is to combine
different types and number of time series so that they yield a matched set of
data points from which coupling or correlation properties can be estimated.
Here, we present multidimensional joint recurrence quantification analysis
(MdJRQA), a recurrence-based technique that allows to analyze coupling
properties between multivariate data sets 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 then test it on simulated
data from linear and nonlinear systems. Finally, we discuss practical issue
regarding the application of the method.
