7.6 Other prospects of the change-point based analysis

The change-points and their "background"

Unless in many other approaches to the analysis of different signal coupling, the information entering the analysis of synchronization in our approach is explicitly represented in the form of elementary, instantaneous events (the change-points). Therefore, the following new ways of the developing the methodology are opened. One may characterize those events by certain features, such as relative change of the monitored index (e.g., the ratio of spectral power in a certain band computed for the adjacent segments), the type of EEG pattern forming the background against which the change-point was found, etc., and then preselect the change-points according to those features before the analysis of synchronization. On the other hand, each of the frequently found synchrocomplex configurations can be separately characterized by the features of their background. Both ways of the analysis may reveal some relations between the background activity and the instants of its change, and the former one also provide the means of improving the quality of the analysis by rejecting less reliable change-points (e.g., too "weak" or found against too "noisy" background).

The change-points and the "external events"

Another promising area of the studies of EEG structure based on the reduction of this signal to the change-point sequences is the analysis of the dependence of instances of change and change-point coupling on the time instances of repetitive "external" events, such as presentation of a stimulus to a subject or his rare and rapid movements (e.g., pressing a response button). The time instants of such events can be determined precisely, and therefore they are widely used as time markers for the analysis of the brain activity which may be in some way related to them (the so-called event-related potentials, event-related desynchronization/synchronization, etc.). The disturbing of the brain activity following these events, however, means that in the studied time interval some rapid changes occur (see Fig. 7.5 for an example of strong event-related change-point); consequently, the common linear indices are not well suited for such intervals, and the change-point based analysis seems to be a rational alternative to them.

The lack of the adaptability of the available change-point detection methods to different time scales and the lack of attention to the change-points caused by its concentration on the segments prevented the realization of this alternative. Only in one work the change-point detection was used for the detection of an "internal" event, the brain activity transformation following, after a certain time delay, an "external" event, the administration of a drug (Deistler et al. 1986), and also only in one work the relationship between the change-points and the external stimuli was studied (Skrylev 1984). The techniques for the estimation of the changes in the probability of the point event, as well as of two near-coinciding events, in the vicinity of a stimulus are, again, developed in the analysis of neuronal spike trains (Palm et al. 1988; Aertsen et al. 1989; Gerstein et al. 1989; Frostig et al. 1990; Lindsey 1997; Awiszus 1997). They provide effective means, in particular, for the identification of fast modulation of synchrony, whereas the analysis of event-related coherency (e.g., Florian et al. 1998) is restricted by the low temporal resolution of coherency estimating. At present, we are only in the beginning of application of those techniques to the EEG change-points.

Combining change-point based and the traditional approaches to the estimation of the synchronization between signals

The most complete understanding of the coupling between nonstationary signals of EEG type can be probably achieved only by the integrated application of different approaches. We found that the basic "topographic" regularities known for correlation and coherency (the dependence of a synchrony index on the interelectrode distance and on the electrode position on the anterior-posterior axis) are well reproduced for the alpha band change-point coincidence index (Fig. 7.10). This on no account can be considered as an evidence for the identity of those indices, because the coincidence of change-points is related to a special type of signal coupling, the structural synchronization, which completely ignores the level of signal synchronization in the intervals between the coinciding change-points. It can be noted, without going into details, that one may expect different relative levels of the linear phase relationship estimates (such as product-moment correlation or coherency) and the change-point synchronization indices when the nature of the signal coupling is different. Hence the use of correlation/coherency estimates in parallel with change-point analysis seems to be quite rational.

More close integration of change-point analysis with the traditional statistic methods may also be advantageous. For instance, the "off-change-point" component of the correlation coefficient, representing the association between two signals not related to their segmentary structure, can be estimated by calculating the correlation coefficient only on the intervals without change-points in both channels and then averaging the obtained values, taking into account the lengths of the intervals as the weights. Conversely, a correlation index may characterize the segmentary structure rather than "off-change-point" component, but, unless the mere change-point synchronization indices, incorporate the values of the characteristic in question (e.g., amplitude or power in the given frequency band) computed for the segments. It can be computed in a following manner: the mean value of the analysed characteristic is computed in each signal channel for each time interval between any neighbouring change-points, with no respect in which channel they were found; this will result in one sequence of means per channel, characterizing the dynamics of the signal; then it only remains to compute the correlation coefficient between the sequences corresponding to different channels.