  Finding the correct encoding for a generic dynamical system's trajectory is a
complicated task: the symbolic sequence needs to preserve the invariant
properties from the system's trajectory. In theory, the solution to this
problem is found when a Generating Markov Partition (GMP) is obtained, which is
only defined once the unstable and stable manifolds are known with infinite
precision and for all times. However, these manifolds usually form highly
convoluted Euclidean sets, are \emph{a priori} unknown, and, as it happens in
any real-world experiment, measurements are made with finite resolution and
over a finite time-span. The task gets even more complicated if the system is a
network composed of interacting dynamical units, namely, a high-dimensional
complex system. Here, we tackle this task and solve it by defining a method to
approximately construct GMPs for any complex system's finite-resolution and
finite-time trajectory. We critically test our method on networks of coupled
maps, encoding their trajectories into symbolic sequences. We show that these
sequences are optimal because they minimise the information loss and also any
spurious information added. Consequently, our method allows us to approximately
calculate the invariant probability measures of complex systems from observed
data. Thus, we can efficiently define complexity measures that are applicable
to a wide range of complex phenomena, such as the characterisation of brain
activity from EEG signals measured at different brain regions or the
characterisation of climate variability from temperature anomalies measured at
different Earth regions.
