Principal component analysis of neuronal ensemble activity reveals multidimensional somatosensory representations

Principal components analysis (PCA) was used to define the linearly dependent factors underlying sensory information processing in the vibrissal sensory area of the ventral posterior medial (VPM) thalamus in eight awake rats. Ensembles of up to 23 single neurons were simultaneously recorded in this area, either during long periods of spontaneous behavior (including exploratory whisking) or controlled deflection of single whiskers. PCA rotated the matrices of correlation between these n neurons into a series of n uncorrelated principal components (PCs), each successive PC oriented to explain a maximum of the remaining variance. The fact that this transformation is mathematically equivalent to the general Hebb algorithm in linear neural networks provided a major rationale for performing it here on data from real neuronal ensembles. Typically, most information correlated across neurons in the ensemble was concentrated within the first 3-8 PCs. Each of these was found to encode distinct, and highly significant informational factors. These factor encodings were assessed in two ways, each making use of fact that each PC consisted of a matrix of weightings, one for each neuron. First, the neurons were rank ordered according to the locations of the central whiskers in their receptive fields, allowing their weightings within different PCs to be viewed as a function of their position within the whisker representation in the VPM. Each PC was found to define a distinctly different topographic mapping of the cutaneous surface. Next, the PCs were used to weight-sum the neurons' simultaneous activities to create population vectors (PVs). Each PV consisted of a single continuous time series which represented the expression of each PC's 'magnitude' in response to stimulation of different whiskers, or during behavioral events such as active tactile whisking. These showed that each PC functioned as a feature detector capable of selectively predicting significant sensory or behavioral events with far greater statistical reliability than could any single neuron. The encoding characteristics of the first few PCs were remarkably consistent across all animals and experimental conditions, including both spontaneous exploration and direct sensory stimulation: PC1 positively weighted all neurons, mainly according to their covariance. Thus it encoded global magnitude of ensemble activity, caused either by combined sensory inputs or intrinsic network activity, such as spontaneous oscillations. PC2 encoded spatial position contrast, generally in the rostrocaudal dimension, across the whole cutaneous surface represented by the ensemble. PC3 more selectively encoded contrast in an orthogonal (usually dorsoventral) dimension. A variable number of higher numbered PCs encoded local position contrast within one or more smaller regions of the cutaneous surface. The remaining PCs typically explained residual 'noise', i.e. the uncorrelated variance that constituted a major part of each neuron's activity. Differences in behavioral or sensory experience produced relatively little in the PC weighting patterns but often changed the variance they explained (eigenvalues) enough to alter their ordering. These results argue that PCA provides a powerful set of tools for selectively measuring neural ensemble activity within multiple functionally significant 'dimensions' of information processing. As such, it redefines the 'neuron' as an entity which contributes portions of its variance to processing not one, but several tasks.