  The detection of phase synchronization of coupled chaotic oscillators which
are not phase-coherent is known to be a challenging task. In this work a method
to detect and measure phase synchronization is presented. The procedure uses
symbol sequence statistics together with Principal Component Analysis (PCA) and
is applied in the phase synchronization analysis of pairs of coupled chaotic
systems with different characteristics. Using PCA, we extract a 3D space
(called latent space) from the original 6D space of the coupled oscillators.
When the oscillators are in complete synchronization, the latent space
represents the dynamics of an isolated oscillator. However, as synchronization
deteriorates, the latent space becomes increasingly disorganized, although it
does retain some level of organization during phase synchronization. A 2D
Poincar\'e-type section is defined in the latent space and the corresponding 1D
map is used to define a non-generating partition such that an arbitrary symbol
sequence is forbidden for any synchronized regime. It is shown that the
probability of occurrence of such a symbol sequence is closely related to the
quality of phase synchronization. The procedure does not require a phase
definition or complicated partitioning algorithms, which is performed by a
simple threshold-crossing technique. This method requires data from different
levels of synchronization to be able to determine the required non-generating
partition.
