Validation in principal components analysis applied to EEG data.

Area of Science:

• Multivariate statistics
• Statistical modeling
• Biomedical data analysis

Background:

• Principal Components Analysis (PCA) is a common multivariate technique.
• Component scores in PCA are subject to sampling variability, particularly with small sample sizes.
• Assessing the stability of PCA component scores is critical but often overlooked.

Purpose of the Study:

• To introduce and validate three novel procedures for assessing Principal Components Analysis (PCA) stability.
• To utilize partial bootstrap confidence regions for evaluating component score variability.
• To enhance the reliability of PCA in small sample scenarios, demonstrated with EEG data.

Main Methods:

• Application of a partial bootstrap method to generate confidence regions for PCA component scores.
• Three validation procedures: assessing score variability via confidence region spread, using centroids as a validation set, and defining the number of significant axes.
• Analysis of electroencephalography (EEG) data from 24 volunteers during a postural control task.

Main Results:

• Two principal axes were retained, explaining 91.6% of the variance in the EEG data.
• Confidence region areas provided insights into score variability, revealing indistinguishable subjects not apparent in principal planes.
• Potential outliers identified in initial analysis were not confirmed by the confidence region method.

Conclusions:

• Partial bootstrap confidence regions offer a robust method for evaluating PCA component score stability.
• The proposed validation procedures improve the interpretability and reliability of PCA, particularly for small datasets.
• This approach enhances the understanding of subject variability in complex datasets like EEG during postural control.