Kernel-based Nonlinear Manifold Learning for EEG Functional Connectivity Analysis with Application to Alzheimer's Disease

Dynamical, causal and cross-frequency coupling analysis using the EEG has received significant interest for the analysis and diagnosis of neurological disorders [1]–[3]. Due to the high computational requirements needed for some of these methods, EEG channel selection is crucial [4]. Functional connectivity (FC) between EEG channels is often used for channel selection and connectivity analysis [4, S, 6]. Ideally, in the case of selecting channels for dynamical and causal analysis, FC methods should be able to account for linear and nonlinear spatial and temporal interactions between EEG channels. In neuroscience, FC is quantified using different measures of (dis) similarity to assess the statistical dependence between two signals [5]. However, the interpretation of FC measures can differ significantly from one measure to another[5, 7]. In the early diagnosis of AD, [7] showed correlations among various (dis)similarity measures, and therefore these measures can be grouped. Thus, one from each is sufficient to extract information from the data [7]. Therefore, the development of a generic measure of (dis)similarity is important in FC analysis.