Bivariable Analysis of EEG Signals - Quantitative EEG Analysis Methods and Clinical Applications - page 119

bottom panel of Figure 4.4. Note the variable degree of synchronization, especially
for example C, which has a large increase of synchronization after second 3.

4.5 Conclusion

In this chapter we applied several linear and nonlinear measures of synchronization
to three typical EEG signals. The first measure we described was the cross-correla-
tion function, which is so far the most often used measure of correlation in neurosci-
ence. We then described how to estimate coherence, which gives an estimation of
the linear correlation as a function of the frequency. In comparison to cross correla-
tion, the advantage of coherence is that it is sensitive to correlations in a limited fre-
quency range. The main limitation of cross correlation and coherence is that they
are linear measures and are therefore not sensitive to nonlinear interactions.
Using the information theory framework, we showed how it is possible to have
a nonlinear measure of synchronization by estimating the mutual information
between two signals. However, the main disadvantage of mutual information is that
it is more difficult to compute, especially with short datasets. Finally, we described
phase synchronization measures to quantify the interdependences of the phases
between two signals, irrespective of their amplitudes. The phases can be computed
using either the Hilbert or the wavelet transform, with similar results.
In spite of the different definitions and sensitivity to different characteristics of
the signals of different synchronization methods, we saw that all of these measures
gave convergent results and that naïve estimations based on visual inspection can be
very misleading. It is not possible in general to assert which is the best synchroniza-
tion measure. For example, for very short datasets mutual information may be not
reliable, but it could be very powerful if long datasets are available. Coherence may
be very useful for studying interactions at particular frequency bands, and phase
synchronization may be the measure of choice if one wants to focus on phase rela-
tionships. In summary, the “best measure” depends on the particular data and
questions at hand.

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