Measurement processes and spatial principal components analysis

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Abstract
Spatial principal components analysis (SPCA) applied to the ongoing EEG yields factor loadings which, when mapped, consistently reveal symmetrical patterns resembling the spherical harmonics. In this paper, we consider the mechanisms responsible for these characteristic patterns. In doing so, we demonstrate that volume conduction is one of a family of processes capable of generating such patterns with SPCA. It is shown that any series of measurements on a sphere in which the covariance is only a function of measurement site angular separation (shift invariant processes) will yield the spherical harmonics as the eigenvectors or factor loadings of the covariance matrix. Simulations further indicate that this effect is robust and not determined by the geometry of the measurement sites. In situations where shift invariant signals coexist with those generated at specific sites (anatomically specific processes), such as evoked potentials and some artifacts, it is shown that the anatomically specific signals do not influence the eigenvectors of the covariance matrix in a uniform or random fashion. The factors most influenced are those whose symmetry is similar to that of the site specific signal.