ABSTRACT
The chapter will cover some of the advanced topics for modeling electroencephalograms with complex structures. We focus in particular on the non-stationarity of epileptic seizure EEGs, which can be manifested in a number of ways such as evolution of the spectra and coherence; and changes in the parameters of time-domain models. Here, we illustrate a procedure for clustering EEG channels based on the similarity of their spectra. Since seizure EEGs are non-stationary, we show that the channel groupings also evolve across the seizure process. Second, we present the FreSpeD method for detecting the points in time when there are changes in either the spectrum or coherence. It is very interesting that the method detected changes in the coherence at precise frequency bands immediately preceding seizure onset. These changes are very subtle. They are not detectable by mere visual inspection and were previously undetected by other methods. Third, we present a different approach to spectral analysis by modeling the EEG as a process that is represented by different states which change over time. Each state is uniquely characterized by a vector autoregressive process. A change in the state implies that there is a change in the EEG process. The fourth topic treats the problem of modeling non-stationary time series from the point of view of finding some optimal model that captures the non-stationarity in the signal. The SLEX method essentially first builds a collection of models where each has a unique SLEX basis and then selects the best model using a complexity-penalized Kullback-Leibler criterion. The fifth topic introduces the new concept of time-varying dual-frequency coherence (e.g., coherence between the alpha oscillation in one channel and the beta oscillation in another channel). This approach is used to analyze the cross-dependence structure between channels during a visual-motor task experiment.
