Quantitative analysis of EEG signals: Time-frequency methods and ...

performed. On one hand, must be large enough in order to give a reliable statistic
and on the other hand if it is too large, it will not be possible to observe fast
changes.
2. The mean and variance for each bin were calculated, and zones in which their
values do not have signicant changes (e.g. less than 20%) were selected.
3. Finally, the corresponding histogram for this zone was constructed, and the normality
of the obtained distribution was veried.
I would like to remark that although the above criterion is arbitrary and does not
prove stationarity 7 , it was very useful as a rst approximation in order to select EEG
data segments to work with, or to reject others with clear non stationary behavior.
However, I would like to stress that in general elaborated statistical criteria can be
hardly fullled by EEG signals. For a more complete discussion about stationarity
related with the application of Chaos methods, see for example Schreiber (1997).
Eckman et al. (1987) presented another approach to the problem of stationarity by
using the so called recurrence plots. Recurrence plots are based on distance calculations
in the phase space. After a phase space reconstruction, the Euclidean distance between
the embedding vectors (lets say N in total) is calculated. Then, an NxN plot is performed
in the following way: for each pair of embedding vectors (i j) (i represented in
the horizontal axis and j in the vertical axis) a point is plotted if its distance is less
than a certain value r. Stationary signals will be characterized by homogeneous plots
and non-stationary signals will show inhomogeneities due to varying features of the embedding
vectors in the phase space. As an example, Fig. 25 shows the recurrence plot
of an stationary one minute EEG signal (see Blanco et al., 1995a).
Recurrence plots give an elegant representation of the stationarity of the signal, but
in many occasions their interpretation is subjective and further analysis is required.
5.4 Short review of Chaos analysis of EEG signals
5.4.1 Correlation Dimension
Since the pioneering work of Babloyantz and coworkers (Babloyantz, 1985), several
groups started to study the dynamics of the brain activity by reconstructing the trajectory
of the system in the phase space and by calculating parameters as the Correlation
Dimension (D 2 ). Low D 2 values correspond to simple systems and high D 2 values to
7 Autocorrelation function is not checked, and the choice of what is considered as stable mean and
variances is in fact arbitrary.
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