Dimension reduction and spatiotemporal regression: applications to neuroimaging

Researchers use spatiotemporal measurements of brain activity obtained from methods such as functional magnetic resonance imaging (MRI), positron emission tomography (PET), and electroencepholagraphy (EEG) in neuroscience to aid in understanding how different regions of the brain respond to stimuli. In a typical experiment, a subject receives some stimulus, such as a visual or auditory cue, and a measuring device, including MRI, PET/SPECT, or electrodes, records measurements of brain activity (as reflected in electrical activity, the level or flow rate of oxygenated blood, or a tracer molecule) for a few seconds afterward at a number of points in the brain. (We analyze data collected using electrodes located on the scalp as an example, but our methodology is independent of precisely how the data are collected.) The experimental data takes the form of a space × time data set that neuroscientists or psychiatrists subsequently analyze. In a simple case, the evidence in favor of or counter to a hypothesis might be entirely spatial (such as the regions of the brain that are most responsive at a given time) or entirely temporal (such as the time delay to peak response or the rate of decay at a given location). More typically, the hypothesis is related to both spatial and temporal variation. For instance, the hypothesis can be that while performing a certain task, one region of the brain activates after 40 milliseconds (msec) while a different region activates after 100 msec. In preliminary work, it might not be possible to specify the anticipated effect in this way, so the goal of analysis becomes more general to characterize differences over space in the temporal waveforms, or differences over time in the spatial activity patterns. In this article, we describe how these two approaches to data analysis can be viewed in a regression context (where the focus is on explaining response characteristics as a function of position in the brain). We demonstrate a general method for describing regression relationships in a parsimonious form using low-dimensional variates (linear functions of highdimensional data). Several statistical procedures abound in spatiotemporal neuroimaging data analysis. For signal detection problems and activation studies, multiple analysis of variance (MANOVA, a classical method that describes a multivariate response as a linear function of several qualitative predictors), DIMENSION REDUCTION AND SPATIOTEMPORAL REGRESSION: APPLICATIONS TO NEUROIMAGING