  Motivated by the recent demonstration of its use as a tool for the detection
and characterization of phase-shape correlations in multivariate time series,
we show that eigenvalue decomposition can also be applied to a matrix of
indices of bivariate phase synchronization strength. The resulting method is
able to identify clusters of synchronized oscillators, and to quantify their
strength as well as the degree of involvement of an oscillator in a cluster.
Since for the case of a single cluster the method gives similar results as our
previous approach, it can be seen as a generalized Synchronization Cluster
Analysis, extending its field of application to more complex situations. The
performance of the method is tested by applying it to simulation data.
