Introducing weighted approaches to study network brain dynamics from EEG epilepsy measurements: The EigenBrain algorithm

It is fairly established that dynamic recordings of functional activity maps can naturally and efficiently be represented by functional connectivity networks. In this article we study weighted and fully-connected brain networks, created from electroencephalographic (EEG) measurements that concern patients with focal and generalized epilepsy. We introduce a totally new methodology that has never been utilized before and that investigates weighted and fully-connected networks, which includes eigen-decomposition analysis, feature extraction and quantitative comparisons among entire graph datasets. Our goal is to establish epileptic seizure detection/prediction rules, by identifying repetitive EEG activity in patients before and after each seizure onset. In the present paper we treat each brain network as a weighted and full adjacency matrix, without cutting, binarizing or ignoring any values. In this way, it is the first time that the full structure of the connectivity weighing profile is exploited. Also apart from graph theory approaches, mathematical models such as eigen-decomposition analysis are used in our research, in order to study and analyze brain networks. Finally, we present and discuss the results and conclusions of our new method, which are in line with earlier EEG epilepsy findings and demonstrate a standard EEG behavior in both the postictal and preictal period.