Generalized Semilinear Canonical Correlation Analysis Applied to the Analysis of Electroencephalogram (EEG) Data

Abstract

Semilinear canonical correlation analysis (SLCCA) is a technique developed by Gregg, Varvel, and Schafer to combine the powers in an electroencephalogram (EEG) power spectrum at each time point. This was used to give a single response that, over all time points, best correlated with a model that describes the response over time to changing levels of a drug in the brain. In this article, we generalize SLCCA so that both sides of the equation now have linear parameters. We call this generalized semilinear canonical correlation analysis (GSLCCA). In this form, it can readily deal with complex treatment structures. These power spectra matrices typically have significant colinearity between columns, which are effectively of reduced rank. We use a data-smoothing approach based on singular value decomposition (SVD) to reduce the dimensionality of these matrices. This increases the efficiency of the algorithm and also improves the results. The model being fitted by GSLCCA is applicable to other areas apart from the analysis of EEG power spectra. As an example of the use of GSLCCA, we use the algorithm to detect pharmacokinetic/pharmacodynamic (PK/PD)-like signals in EEG power spectra, and to obtain drug “signatures” (i.e., loadings in CCA terminology), which can be readily compared for different drugs, as detecting drug entry into the brain is important clinically.

Key Words:

• Data matrix approximation
• Modeling
• Nonlinear regression
• Singular value decomposition

Acknowledgments

We thank the referees for their many helpful comments that considerably improved the article.