title: Validation in principal components analysis applied to EEG data.
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.
authors.affiliation: Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, Brazil.
authors.forename: João Carlos G D
authors.initials: JC
authors.lastname: Costa
authors.affiliation: Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, Brazil.
authors.forename: Paulo José G
authors.initials: PJ
authors.lastname: Da-Silva
authors.affiliation: Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, Brazil.
authors.forename: Renan Moritz V R
authors.initials: RM
authors.lastname: Almeida
authors.affiliation: Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, Brazil.
authors.forename: Antonio Fernando C
authors.initials: AF
authors.lastname: Infantosi
mesh_terms: D000328:Adult; D004569:Electroencephalography / Q000379:methods*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D015999:Multivariate Analysis; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012107:Research Design; D018401:Sample Size; D012815:Signal Processing, Computer-Assisted; D055815:Young Adult