Topographic components analysis of evoked potentials: estimation of model parameters and evaluation of parameter uniqueness.

The purpose of this paper is to evaluate the practicability of the 'topographic components model' proposed by Möcks for the spatio-temporal characterization of multi-channel evoked potentials (EP), and to present a complete and detailed algorithm for this method of analysis. Details of the algorithm are discussed along with various computational issues, especially with regard to contrasts with traditional principal components analysis. The algorithm is applied to multi-channel pattern-shift visual EP data obtained from normal subjects, and the model is demonstrated to provide data reduction of 71% with a relative mean-squared error (MSE) of 2%. Obvious features of the data are seen to be reflected in the estimated model parameters, lending support to the appropriateness of the model. The results also demonstrate that although the model parameters are uniquely identifiable in theory, care must be taken when fitting the model to insure that the MSE is not so insensitive to perturbations in the model parameters that they are rendered 'non-unique' for all practical purposes. The proper selection of model order is shown to play a critical role in avoiding this problem. Finally, a theoretical analysis is presented which evaluates the relationship between parameter 'uniqueness', model order, and the non-orthogonality of the model components.