Using spatiotemporal source separation to identify prominent features in multichannel data without sinusoidal filters

The number of simultaneously recorded electrodes in neuroscience is steadily increasing, providing new opportunities for understanding brain function, but also new challenges for appropriately dealing with the increase in dimensionality. Multivariate source-separation analysis methods have been particularly effective at improving signal-to-noise ratio while reducing the dimensionality of the data, and are widely used for cleaning, classifying, and source-localizing multichannel neural time series data. Most source-separation methods produce a spatial component (that is, a weighted combination of channels to produce one time series); here, this is extended to apply sourceseparation to a time series, with the idea of obtaining a weighted combination of successive time points, such that the weights are optimized to satisfy some criteria. This is achieved via a two-stage source-separation procedure, in which an optimal spatial filter is first constructed, and then its optimal temporal basis function is computed. This second stage is achieved with a time-delay-embedding matrix, in which additional rows of a matrix are created from time-delayed versions of existing rows. The optimal spatial and temporal weights can be obtained by solving a generalized eigendecomposition of covariance matrices. The method is demonstrated in simulated data and in an empirical EEG study on theta-band activity during response conflict. Spatiotemporal source separation has several advantages, including defining empirical filters without the need to apply sinusoidal narrowband filters.