NIC Series Volume 24:   Synchronization and Interdependence Measures and their Applications to the Electroencephalogram of Epilepsy Patients and Clustering of Data Alexander Kraskov   ISBN 3-00-013619-3 May 2004, 106 pages   PDF

The main goals of this thesis are the comparative investigation, further development and improvement, and application of different measures of synchronization.

In this thesis four different classes of the synchronization measures are compared with each other. These measures comprised the linear crosscorrelation, measures with information theoretic background such as mutual information and transfer entropy, phase synchronization measures based on either Hilbert or wavelet transform, and measures of generalized synchronization.

For mutual information and transfer entropy a new family of estimators is developed. Their major advantage lies in vastly reduced systematic errors, when compared to previous estimators. This allows to use them on very small data sets. It also makes possible their use in independent component analysis to estimate absolute values of mutual dependencies.

A theoretical comparison of the two phase extraction methods based on Hilbert and wavelet transform is derived in the second part of this thesis.

Since pathological processes such as epilepsy are considered to be related to synchronization phenomena, all the measures of synchronization are applied in the third part of this thesis to the analysis of intracranial EEG recordings from epilepsy patients undergoing pre-surgical diagnostics. In this study we address the question whether it is possible to identify the location of an epileptic focus from an EEG recorded during the seizure-free interval.

More generally, synchronization is just one way how systems can show dependencies. Finding dependencies between different (sub-)systems and classifying these systems based on the levels of dependencies among them is an important problem surpassing synchronization. Therefore, studying general dependencies and clustering data based on them constituted another part of the thesis. In this part we introduce a new, conceptually very simple and natural, hierarchical clustering algorithm, called mutual information clustering (MIC). We illustrate our method with several applications. Among them are clustering of DNA sequences of mammals and clustering of minimally dependent components of the ECG of a pregnant woman.