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Nonstationary phenomena are present in EEG usually in the form of transient events, such as sharp waves, spikes or spike-wave discharges which are characteristic for the epileptic EEG, or as alternation of relatively homogenous intervals (segments) with different statistical features (e.g., with different amplitude or variance) (Lopes da Silva 1978). The transient phenomena have specific pattern which makes it possible to identify them by visual inspection easily in most cases, whereas the identification of the homogenous segments of EEG requires a certain theoretical basis.
To perform the computerized analysis of an EEG record, it is converted into digital form. This means
that a quanted process is constructed from the signal which is continuous in its original form. The
sampling (digitizing) rate typically lies between 60 and 200 Hz, allowing spectral estimating in the
traditional range from 1 to 30 Hz, which includes most of the prominent components of the EEG.
Accordingly, if about 50--100 samples are necessary for a sound statistical estimation, there is no sense
to check the EEG intervals with less than 0.5--1 s duration for stationarity. If the EEG requires
further fragmentation to obtain stationary segments, consistent statistical estimates for so short
segments could not be obtained and the question of their stationarity would be senseless.
Assuming that the duration of a minimal stationary interval usually is no less than 2 s, as reported in (McEwen & Anderson 1975), the procedure of EEG segmentation into stationary fragments would consist of four stages. At the first stage, an EEG recording is divided preliminary into equal "elementary" segments of 2 s length. Then, each segment is characterized by a certain set of features, e.g., spectral estimations. At the third stage, using one of the multivariate statistical procedures, the elementary EEG segments are ascribed to one of a number of classes accordingly to their characteristics. Finally, the bounds between the segments belonging to a same class are erased. Thus, the EEG recording is transformed into a series of segments within which the EEG parameters remain relatively constant. Each of these stationary segments is characterized by its specific duration and typological features. If the number of segment types in the real EEG is not too high, the idea of piecewise stationary organization of the EEG will offer explicit advantages over the alternative primary concept of the EEG as a continuous stationary stochastic process.
This "fixed-interval" approach to the EEG segmentation was used in early works concerned with EEG segmentation (Giese et al. 1979; Jansen et al. 1979; Jansen et al. 1981; Barlow 1985). The number of typical EEG segments really turned out to be restricted, not more than 15--35 for different EEGs (Giese et al. 1979; Jansen et al. 1979; Jansen et al. 1981), and the duration of the majority of segments did not exceed 4 s, which provided evidence for the piecewise EEG organization.
However, this segmentation method had a serious disadvantage that some of the fixed intervals should necessary fall on boundaries between the real stationary EEG segments. This led to the appearance of a variety of EEG fragments which contained transition processes and, hence, were not strictly stationary. In addition, the boundaries between stationary segments were defined rather roughly, with the accuracy no better than the duration of the fixed interval.
To overcome these disadvantages, it was necessary to develop a segmentation procedure including adaptation of the segment boundaries to the real positions of the transitions between stationary intervals. This methodology, called adaptive segmentation, was applied, in one form or another, in the majority of methods of the automatic detection of stationary segments in the EEG (Barlow 1985).
Let us now consider the main approaches to the adaptive segmentation of the EEG signal.