| Wavelet neural networks (WNNs) are introduced as a new class of elliptic basis function neural networks and wavelet networks, and are applied to the numerical modeling and classification of EEGs. The implementation of the networks is achieved in two possibly cyclical stages of structure and parameter identification. For structure identification, two methods are developed: one generic, based on data clusterings, and one specific, using wavelet analysis. For parameter identification, two methods are also implemented: the Levenberg-Marquardt algorithm and a genetic algorithm of ranking type.; The problem of model generalization is considered from both, a crossvalidation and a regularization point of view. For the latter, a corrected average squared error (CASE) is derived as a new model selection criterion that does not rely on assumptions about error distributions or modeling paradigms.; For EEG modeling, the nonlinear dynamics framework is employed in the reconstruction of state-spaces via the embedding scheme. Preprocessing for the resulting state-vector is introduced in terms of decorrelation and compression. The naive application of chaos theory to EEGs is shown to be useful in feature extraction, but not in corroborating theories about the nature of EEGs. For the latter, the concept of modeling resolution is introduced. It is shown that the chaos-in-the-brain question becomes meaningful only as a function of modeling resolution.; For EEG classification, a general WNN classification system is implemented as a cascade of synergistic feature selection, WNN nonlinear discrimination, and decision logic. A feature library is described including raw and model-based features, ranging from traditional measures to chaotic indicators. Training for maximum-likelihood classification is shown to be inductively feasible via a decoder-type WNN classifier adjusted with nonanalytic methods.; WNNs were found to be ideally suited for problems of EEG analysis due to the long-duration/low-frequency and short-duration/high-frequency structure of EEG signals. |
