title: The LDA beamformer: Optimal estimation of ERP source time series using linear discriminant analysis.
abstract: We introduce a novel beamforming approach for estimating event-related potential (ERP) source time series based on regularized linear discriminant analysis (LDA). The optimization problems in LDA and linearly-constrained minimum-variance (LCMV) beamformers are formally equivalent. The approaches differ in that, in LCMV beamformers, the spatial patterns are derived from a source model, whereas in an LDA beamformer the spatial patterns are derived directly from the data (i.e., the ERP peak). Using a formal proof and MEG simulations, we show that the LDA beamformer is robust to correlated sources and offers a higher signal-to-noise ratio than the LCMV beamformer and PCA. As an application, we use EEG data from an oddball experiment to show how the LDA beamformer can be harnessed to detect single-trial ERP latencies and estimate connectivity between ERP sources. Concluding, the LDA beamformer optimally reconstructs ERP sources by maximizing the ERP signal-to-noise ratio. Hence, it is a highly suited tool for analyzing ERP source time series, particularly in EEG/MEG studies wherein a source model is not available.
authors.affiliation: Neurotechnology Group, Technische Universität Berlin, Germany; Behavioural & Clinical Neuroscience Institute, Department of Psychiatry, University of Cambridge, UK. Electronic address: matthias.treder@gmail.com.
authors.forename: Matthias S
authors.initials: MS
authors.lastname: Treder
authors.affiliation: Machine Learning Laboratory, Technische Universität Berlin, Germany.
authors.forename: Anne K
authors.initials: AK
authors.lastname: Porbadnigk
authors.affiliation: Machine Learning Laboratory, Technische Universität Berlin, Germany.
authors.forename: Forooz
authors.initials: F
authors.lastname: Shahbazi Avarvand
authors.affiliation: Machine Learning Laboratory, Technische Universität Berlin, Germany; Department of Brain and Cognitive Engineering, Korea University, Seoul, Republic of Korea. Electronic address: klaus-robert.mueller@tu-berlin.de.
authors.forename: Klaus-Robert
authors.initials: KR
authors.lastname: Müller
authors.affiliation: Neurotechnology Group, Technische Universität Berlin, Germany. Electronic address: benjamin.blankertz@tu-berlin.de.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Blankertz
mesh_terms: D000465:Algorithms; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D016002:Discriminant Analysis; D004569:Electroencephalography; D005071:Evoked Potentials / Q000502:physiology*; D006801:Humans; D015225:Magnetoencephalography; D008959:Models, Neurological; D012815:Signal Processing, Computer-Assisted