A Kernel-based Nonlinear Manifold Learning for EEG Channel Selection with Application to Alzheimer's Disease

For the characterisation and diagnosis of neurological disorders, dynamical, causal and crossfrequency coupling analysis using the EEG has gained considerable attention. Due to high computational costs in implementing some of these methods, the selection of important EEG channels is crucial. The channel selection method should be able to accommodate non-linear and spatiotemporal interactions among EEG channels. In neuroscience, different measures of (dis)similarity are used to quantify functional connectivity between EEG channels. Brain regions functionally connected under one measure do not necessarily imply the same with another measure, as they could even be disconnected. Therefore, developing a generic measure of (dis)similarity is important in channel selection. In this paper, learning of spatial and temporal structures within the data is achieved by using kernel-based nonlinear manifold learning, where the positive semi-definite kernel is a generalisation of various (dis)similarity measures. We introduce a novel EEG channel selection method to determine which channel interrelationships are more important for the in-depth neural dynamical analysis, such as understanding the effect of neurodegeneration, e.g. Alzheimers disease (AD), on global and local brain dynamics. The proposed channel selection methodology uses kernel-based nonlinear manifold learning via Isomap and Gaussian Process Latent Variable Model (Isomap-GPLVM). The Isomap-GPLVM method is employed to learn the spatial and temporal local similarities and global dissimilarities present within the EEG data structures. The resulting kernel (dis)similarity matrix is used as a measure of synchrony, i.e. linear and nonlinear functional connectivity, between EEG channels. Based on this information, linear Support Vector Machine (SVM) classification with Monte-Carlo cross-validation is then used to determine the most important spatio-temporal channel inter-relationships that can well distinguish a group of patients from a cohort of age-matched healthy controls (HC). In this work, the analysis of EEG data from HC and patients with mild to moderate AD is presented as a case study. Considering all pairwise EEG channel combinations, our analysis shows that functional connectivity between bipolar channels within temporal, parietal and occipital regions can distinguish well between mild to moderate AD and HC groups. Furthermore, while only considering connectivity with respect to each EEG channel. Our results indicate that connectivity of EEG channels along the fronto-parietal with other channels are important in diagnosing mild to moderate AD.