A resampling method for estimating the signal subspace of spatio-temporal EEG/MEG data

Abstract

Source localization using spatio-temporal electroencephalography (EEG) and magnetoencephalography (MEG) data is usually performed by means of signal subspace methods. The first step of these methods is the estimation of a set of vectors that spans a subspace containing as well as possible the signal of interest. This estimation is usually performed by means of a singular value decomposition (SVD) of the data matrix: The rank of the signal subspace (denoted by r) is estimated from a plot in which the singular values are plotted against their rank order, and the signal subspace itself is estimated by the first r singular vectors. The main problem with this method is that it is strongly affected by spatial covariance in the noise. Therefore, two methods are proposed that are much less affected by this spatial covariance, and old and a new method. The old method involves prewhitening of the data matrix, making use of an estimate of the spatial noise covariance matrix. The new method is based on the matrix product of two average data matrices, resulting from a random partition of a set of stochastically independent replications of the spatio-temporal data matrix. The estimated signal subspace is obtained by first filtering out the asymmetric and negative definite components of this matrix product and then retaining the eigenvectors that correspond to the r largest eigenvalues of this filtered data matrix. The main advantages of the partition-based eigen decomposition over prewhited SVD is that 1) it does not require an estimate of the spatial noise covariance matrix and 2b) that it allows one to make use of a resampling distribution (the so-called partitioning distribution) as a natural quantification of the uncertainty in the estimated rank. The performance of three methods (SVD with and without prewhitening, and the partition-based method) is compared in a simulation study. From this study, it could be concluded that prewhited SVD and the partition-based eigen decomposition perform equally well when the amplitude time series are constant, but that the partition-based method performs better when the amplitude time series are variable.