Orthogonal expansions: their applicability to signal extraction in electrophysiological mapping data

The applicability of orthogonal expansions (singular-value decomposition, Karhunen-Loève transform and principal-component analysis) for the purpose of identifying source distributions associated with definite electrophysiological events in the heart and brain is explored with a current dipole source model. By definition, the expansion eigenvectors are orthogonal, and as such will extract the features of one specific source only if all other secondary signals are orthogonal to that first source. The number of significant eigenvectors can be related to the number of original components forming a signal, but there is not a one-to-one correspondence between these eigenvectors and the individual components. Furthermore, many eigenvectors may be needed to faithfully represent even a single source, if that source is nonstationary. We conclude that generally it would be inappropriate to ascribe any physiological significance to the data resulting from such expansions.