Modeling the variability of electrical activity in the brain

This thesis investigates the analysis of brain electrical activity. An important challenge is the presence of large variability in neuroelectrical recordings, both across different subjects and within a single subject, for example across experimental trials. We propose a new method called adaptive waveform learning (AWL). It is general enough to include all types of relevant variability empirically found in neuroelectric recordings, but it can be specialized for different concrete settings to prevent from overfitting irrelevant structures in the data. The first part of this work gives an introduction into the electrophysiology of the brain, presents frequently used recording modalities, and describes state-of-the-art methods for neuroelectrical signal processing. The main contribution of the thesis consists in three chapters introducing and evaluating the AWL method. We first provide a general signal decomposition model that explicitly includes different forms of variability across signal components. This model is then specialized for two concrete applications: processing a set of segmented experimental trials and learning repeating structures across a single recorded signal. Two algorithms are developed to solve these models. Their efficient implementations, based on alternate minimization and sparse coding techniques, allow the processing of large datasets. The proposed algorithms are evaluated on both synthetic data and real data containing epileptiform spikes. Their performances are compared to those of PCA, ICA, and template matching for spike detection.