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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 413801, 10 pages
http://dx.doi.org/10.1155/2014/413801
Research Article

Validation in Principal Components Analysis Applied to EEG Data

Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, Brazil

Received 1 May 2014; Revised 13 August 2014; Accepted 14 August 2014; Published 8 September 2014

Academic Editor: Ezequiel López-Rubio

Copyright © 2014 João Carlos G. D. Costa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The well-known multivariate technique Principal Components Analysis (PCA) is usually applied to a sample, and so component scores are subjected to sampling variability. However, few studies address their stability, an important topic when the sample size is small. This work presents three validation procedures applied to PCA, based on confidence regions generated by a variant of a nonparametric bootstrap called the partial bootstrap: (i) the assessment of PC scores variability by the spread and overlapping of “confidence regions” plotted around these scores; (ii) the use of the confidence regions centroids as a validation set; and (iii) the definition of the number of nontrivial axes to be retained for analysis. The methods were applied to EEG data collected during a postural control protocol with twenty-four volunteers. Two axes were retained for analysis, with 91.6% of explained variance. Results showed that the area of the confidence regions provided useful insights on the variability of scores and suggested that some subjects were not distinguishable from others, which was not evident from the principal planes. In addition, potential outliers, initially suggested by an analysis of the first principal plane, could not be confirmed by the confidence regions.