Summary
We describe a substantive application of the trilinear topographic components /parallel factors model (TC/PARAFAC, due to Möcks/Harshman) to the decomposition of multichannel evoked potentials (MEP's). We provide practical guidelines and procedures for applying PARAFAC methodology to MEP decomposition. Specifically, we apply techniques of data preprocessing, orthogonality constraints, and validation of solutions in a complete TC analysis, for the first time using actual MEP data. The TC model is shown to be superior to the traditional bilinear principal components model in terms of data reduction, confirming the advantage of the TC model's added assumptions. The model is then shown to provide a unique spatiotemporal decomposition that is reproducible in different subject groups. The components are shown to be consistent with spatial/temporal features evident in the data, except for an artificial component resulting from latency jitter. Subject scores on this component are shown to reflect peak latencies in the data, suggesting a new aspect to statistical analyses based on subject scores. In general, the results support the conclusion that the TC model is a promising alternative to principal components for data reduction and analysis of MEP's.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bio-logic Systems Corp. Guidelines for Normative Data Collection: Brain Atlas Systems. Mundelein, Illinois, July 1988.
Carroll, J. D. and Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of "Eckart-Young" decomposition. Psychometrika, 1970, 35:283–319.
Carroll, J. D. and Pruzansky, S. The CANDECOMP-CANDELINC family of models and methods for multidimensional data analysis. In: Law, H. G., Snyder, Jr., C. W., Hattie, J. A., and McDonald, R. P. (eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984: 372–402.
Donchin, E. and Heffley, E. F. Multivariate analysis of event-related potential data: A tutorial review. In: Otto, D. A. (ed.), Multidisciplinary Perspectives in Event-Related Brain Potential Research, U.S. Gov. Printing Office, Washington, DC, 1978: 555–572.
Field, A. S. Applied Topographic Component / Parallel Factor Analysis for Spatiotemporal Decomposition of Multichannel Evoked Potentials. Ph.D. thesis, Department of Bioengineering, University of Illinois at Chicago, 1991.
Field, A. S. and Graupe, D. Topographic components analysis of evoked potentials: Estimation of model parameters and evaluation of parameter uniqueness. J. Biomed. Eng., 1990a, 12:287–300.
Field, A. S. and Graupe, D. Topographic components analysis of evoked potentials: Parameter estimation and some preliminary results. Proc. IEEE Int. Symp. Circ. Syst. (ISCAS), New Orleans, 1990b: 2049–2052.
Glaser, E. M. and Ruchkin, D. S. Principles of Neurobiological Signal Analysis. Academic Press, New York, 1976: 233–290.
Harner, R. N. Singular value decomposition-A general linear model for analysis of multivariate structure in the electroencephalogram. Brain Topography, 1990, 3:43–47.
Harshman, R. A. Foundations of the PARAFAC procedure: Models and conditions for an ‘explanatory’ multi-modal factor analysis. UCLA Working Papers in Phonetics (University Microfilms #10,085), 1970, 16:1–84.
Harshman, R. A. ‘How can I know if it's "real?"’ A catalog of diagnostics for use with three-mode factor analysis and multidimensional scaling. In: Law, H. G., Snyder, Jr., C. W., Hattie, J. A., and McDonald, R. P. (eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984: 566–591.
Harshman, R. A. and De Sarbo, W. S. An application of PARAFAC to a small sample problem, demonstrating preprocessing, orthogonality constraints, and split-half diagnostic techniques. In: Law, H. G., Snyder, Jr., C. W., Hattie, J. A., and McDonald, R. P. (eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984, 602–642.
Harshman, R. A. and Lundy, M. E. Data preprocessing and the extended PARAFAC model. In: Law, H. G., Snyder, Jr., C. W., Hattie, J. A., and McDonald, R. P. (eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984a: 216–281.
Harshman, R. A. and Lundy, M. E. The PARAFAC model for three-way factor analysis and multidimensional scaling. In: Law, H. G., Snyder, Jr., C. W., Hattie, J. A., and McDonald, R. P. (eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984b: 123–215.
Lehmann, D. Principles of spatial analysis. In: Gevins, A. S. and Remond, A. (eds.), Methods of Analysis of Brain Electrical and Magnetic Signals, volume 1 of Handbook of Electroencephalography and Clinical Neurophysiology (Revised Series), Elsevier, Amsterdam, 1987: 309–354.
Lundy, M. E. and Harshman, R. A. Reference Manual for the PARAFAC Analysis Package. Scientific Software Associates, London, Ontario, Canada, 1985.
Möcks, J. The influence of latency jitter in principal component analysis of event-related potentials. Psychophysiol., 1986, 23:480–484.
Möcks, J. Decomposing event-related potentials: A new topographic components model. Biol. Psychol., 1988a, 26:199–215.
Möcks, J. Topographic components model for event-related potentials and some biophysical considerations. IEEE Trans. Biomed. Eng., 1988b, 35:482–484.
Möcks, J. and Verleger, R. Principal component analysis of event-related potentials: A note on misallocation of variance. Electroenceph. Clin. Neurophysiol., 1986, 65:393–398.
Nunez, P. L. Electric Fields of the Brain. Oxford Univ. Press, New York, 1981: 22–24.
Offner, F. F. The EEG as potential mapping: The value of the average monopolar reference. Electroenceph. Clin. Neurophysiol., 1950, 2:215–216.
Rabiner, L. R. and Schafer, R. W. Digital Processing of Speech Signals. Prentice-Hall, New Jersey, 1978: 480–484.
Skrandies, W. Data reduction of multichannel fields: Global field power and principal component analysis. Brain Topography, 1989, 2:73–80.
Skrandies, W. and Lehmann, D. Spatial principal components of multichannel maps evoked by lateral visual half-field stimuli. Electroenceph. Clin. Neurophysiol., 1982, 54:662–667.
Wood, C. C. and McCarthy, G. Principal component analysis of event-related potentials: Simulation studies demonstrate misallocation of variance across components. Electroenceph. Clin. Neurophysiol., 1984, 59:249–260.
Author information
Authors and Affiliations
Additional information
This paper contains portions of the first author's dissertation, submitted in partial fulfillment of the requirements for the Ph.D. degree, Department of Bioengineering, University of Illinois at Chicago. The authors are indebted to G. Raviv of Bio-logic Systems Corp., Mundelein, Illinois, USA, for providing proprietary data and topographic mapping software used in this research; R. A. Harshman and M. E. Lundy of Scientific Software Associates, London, Ontario, Canada, for advising on the use of the PARAFAC analysis package; the Computer Center of the University of Illinois at Chicago for providing computational and plotting facilities; J. Kripal for helping to collect the data; and M. Field for assisting with the manuscript. They also thank R. A. Harshman and anonymous reviewers for their comments on an earlier draft of the paper.
Rights and permissions
About this article
Cite this article
Field, A.S., Graupe, D. Topographic component (Parallel Factor) analysis of multichannel evoked potentials: Practical issues in trilinear spatiotemporal decomposition. Brain Topogr 3, 407–423 (1991). https://doi.org/10.1007/BF01129000
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01129000