TY - JOUR
T1 - The LDA beamformer
T2 - Optimal estimation of ERP source time series using linear discriminant analysis
AU - Treder, Matthias S.
AU - Porbadnigk, Anne K.
AU - Shahbazi Avarvand, Forooz
AU - Müller, Klaus Robert
AU - Blankertz, Benjamin
N1 - Funding Information:
We would like to thank Marieke Mur and Taylor Schmitz for insightful comments on the manuscript. The research leading to this results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement number 611570 , the BK21 program of NRF , BMBF grants 01GQ0850 , 01IS14013A-E and 01GQ1115 , and DFG grant MU 987/19-1 . Correspondence to MST, KRM, and BB.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84956884007&partnerID=8YFLogxK
U2 - 10.1016/j.neuroimage.2016.01.019
DO - 10.1016/j.neuroimage.2016.01.019
M3 - Article
C2 - 26804780
AN - SCOPUS:84956884007
SN - 1053-8119
VL - 129
SP - 279
EP - 291
JO - NeuroImage
JF - NeuroImage
ER -