Methods to extract multi-dimensional features of event-related brain activities from EEG data

Abstract

Cognitive processes are studied, among others, by analyzing event-related potentials/oscillations (ERPs/EROs) with various signal processing techniques. The commonly used processing techniques have, however, various limitations. For example, temporal principal component analysis (t-PCA) assumes, contrary to the actual situation, that waveforms of the PCA-extracted component for all subjects are the same. Also, several PCA-extracted components cannot be analyzed simultaneously since their amplitudes and polarities are diversiform. Moreover, conventional time-frequency analysis (TFA) can not effciently distinguish between evoked EROs mixed in temporal and spectral domains. Additionally, induced EROs are usually investigated using TFA, which ignores the interactions of induced EROs in temporal, spectral, and spatial domains. This thesis develops some EEG analysis algorithms and provides novel frameworks to investigate the cognitive mechanisms of ERPs/EROs. Specifcally, in the frst study, to address the problems in t-PCA, we introduce back-projection theory into t-PCA for solving the problem that several extracted components fail to be analyzed simultaneously. ERPs are extracted from single-trial EEG of an individual subject to address the unreasonable hypothesis in the group PCA analysis. In the second study, we explore evoked EROs to study some cognitive process stages that have not been explained accurately before. This is achieved by frst extracting the ERPs of interest in the time domain using t-PCA and then transforming the reconstructed waveforms of ERPs into time-frequency representations (TFRs). In the third study, we exploit canonical polyadic tensor decomposition to analyze the multi-domain features of induced EROs from the fourth-order tensor formed by TFRs of single-trial EEG data. This enables us to reveal potential interactions of different modes in induced EROs. In conclusion, the thesis introduces some new signal processing techniques and novel frameworks to study the dynamics of ERPs/EROs effciently, which are validated using actual and synthetic EEG/ERP data. Keywords: Event-related potentials/oscillations, principal component analysis, time-frequency analysis, tensor decomposition.