Validation in Principal Components Analysis Applied to EEG Data
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...
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doaj-630d0d34b7e54dada4714d24bb2c91632020-11-25T00:24:43ZengHindawi LimitedComputational and Mathematical Methods in Medicine1748-670X1748-67182014-01-01201410.1155/2014/413801413801Validation in Principal Components Analysis Applied to EEG DataJoão Carlos G. D. Costa0Paulo José G. Da-Silva1Renan Moritz V. R. Almeida2Antonio Fernando C. Infantosi3Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, BrazilBiomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, BrazilBiomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, BrazilBiomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, BrazilThe 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.http://dx.doi.org/10.1155/2014/413801 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
João Carlos G. D. Costa Paulo José G. Da-Silva Renan Moritz V. R. Almeida Antonio Fernando C. Infantosi |
spellingShingle |
João Carlos G. D. Costa Paulo José G. Da-Silva Renan Moritz V. R. Almeida Antonio Fernando C. Infantosi Validation in Principal Components Analysis Applied to EEG Data Computational and Mathematical Methods in Medicine |
author_facet |
João Carlos G. D. Costa Paulo José G. Da-Silva Renan Moritz V. R. Almeida Antonio Fernando C. Infantosi |
author_sort |
João Carlos G. D. Costa |
title |
Validation in Principal Components Analysis Applied to EEG Data |
title_short |
Validation in Principal Components Analysis Applied to EEG Data |
title_full |
Validation in Principal Components Analysis Applied to EEG Data |
title_fullStr |
Validation in Principal Components Analysis Applied to EEG Data |
title_full_unstemmed |
Validation in Principal Components Analysis Applied to EEG Data |
title_sort |
validation in principal components analysis applied to eeg data |
publisher |
Hindawi Limited |
series |
Computational and Mathematical Methods in Medicine |
issn |
1748-670X 1748-6718 |
publishDate |
2014-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2014/413801 |
work_keys_str_mv |
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