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We consider now change-points in different components of the frequency spectrum of typical EEG signal. An example given in Fig. 7.2 represents the following characteristic features of signal structure and results of change-point detection. Only few change-points in power are found in the initial EEG (unless a prominent alpha rhythm is present). Not many change-points are found after filtering in the bands of slow rhythm, called delta (b) and theta (c), which usually have no prominent time structure. The variations of the bandwidth usually not affect the number of detected change-points strongly. When slow rhythms make a considerable contribution to the total EEG power, its dynamics usually also has no clear time structure, and only few change-points could be found. After filtering in alpha (d) and beta (e) bands, on the contrary, a high number of change-points is found; the most clear modulations marked by change-points are in the alpha band. The relatively clear time structure of alpha activity is not a new fact, yet it is important to be mentioned because of high sensitivity of the alpha band to fine changes in brain state (Lehmann 1980). The change-points in this band therefore provide a useful tool for the brain state monitoring, and we concentrated on them most attention in our work.
Fig. 7.2. Change-points in different frequency components of the EEG
EEG (subject tw12, eyes closed, no task) and the change-points
From the top down: the original signal; the signal after digital filtering with bandpasses 3.5--7.5 Hz (theta), 8--12 Hz (alpha) and 14--21 Hz (low beta). Change-point detection was made in all these sequences (after squaring) with the same parameters. The "false alarm" probability at the final stage of detection was 0.2 for intervals longer than 100 samples and 0.1 to 0.05 for shorter intervals. The EEG was recorded from right occipital electrode (standard position O2). Horizontal scale: 1 s.
The change-points in Fig. 7.2 follow the visually distinct modulations of the filtered signal, with no respect to a frequency band. Unfortunately, the "actual" position of a change-point in real EEG in most cases cannot be located. This is due to the lack of understanding of the EEG genesis; in particular, very little is known about the "events" in the brain tissues causing transformations of the dynamics of on-going EEG. Therefore verifying the detected change-points in the EEG is possible only on the basis of a standard method of change-point detection, which is currently unavailable. On the other hand, the experience of researchers and clinical electroencephalographists suggests that the visually distinct modulations of the EEG signal and its components are highly informative. This is why the visual control was found to be quite appropriate for the estimation of the quality of change-point detection.
Specifically, we inspected visually the EEG, both unprocessed and filtered, with the marks of the change-points detected in the alpha band power, which gives a sufficient impression of the correspondence of the detected change-points to the visible changes in the EEG alpha activity. This way we checked the validity of change-points found in 138 one-minute EEG recordings (7680 samples per recording), obtained from different subjects in various conditions. Although the automatic search for change-points was carried out in all the EEGs without any tuning of any parameters of the detection procedure, it was found that vast majority of detected change-points corresponded to real changes in alpha activity, and that most of visually distinct modulations of alpha activity were found by the program. Note that almost all the other known methods of EEG segmentation cannot work in such unsupervised regime and require the manual adjusting of the detection threshold for satisfactory detection of changes in EEG recordings with considerably different characteristics. In our program, the threshold was tuned completely automatically according to the "false alarm" probabilities defined for all the set of EEGs.
Fig. 7.3. Change-points in different types of the EEG alpha activity without substantial gradual changes
Change-points in different types of the EEG alpha activity without substantial gradual changes: (a) EEG with high amplitude, weakly modulated alpha rhythm (subject tw07); (b) EEG with well modulated alpha rhythm (tw09); (c) EEG with relatively low amplitude alpha rhythm (tw11). Upper and lower curves in each pair are original and filtered (7.5--12.5 Hz) EEG, correspondingly. EEG was recorded from right occipital electrode (O2) in eyes closed, rest condition. The vertical lines are the change-points detected in the basic diagnostic sequence. Horizontal scale: 1 s. (From Shishkin & Kaplan, in press).
Fig. 7.3 gives three examples of EEG representing various types of normal (physiological) alpha activity from our set of recordings. In the first example, the alpha rhythm makes main contribution to the total EEG; it has high power but is only slightly modulated. In the second example, the contribution of the alpha rhythm is also rather high, but it is strongly modulated and sometimes almost disappear. In the third example, the alpha band activity is at a low level most of time. As can be seen from Fig. 7.3, the program reliably detected the change-points despite of such variety of signal patterns.
Fig. 7.4. Change-points in alpha activity (7.5--12.5 Hz) with gradual changes
Subject tw03, eyes closed, rest condition. Right occipital electrode (O2). The change-points (vertical lines) were detected in the basic diagnostic sequence. Horizontal scale: 1 s.
The changes of amplitude/power of the alpha rhythm in the EEG shown in Fig. 7.3 were rather abrupt. Fig. 7.4 presents a more challenging type of pattern, where abrupt changes in the alpha activity dynamics are almost absent, and the consistency with the piecewise stationary model is hardly possible. Even in this case, however, the change-points most often indicate short term transition processes and separate intervals with different level of activity (different amplitude/power in alpha band), and some approximation of the EEG structure is also obtained. Thus, the detected change-points are, undoubtedly, of practical value, though the question of how much the components of the EEG is in agreement with the piecewise stationary model remains to be answered.