Dimensionality choice in principal components analysis via cross-validatory methods

• K + E is most accurate in determining the appropriate number of components in a PCA.
• Modified K + E performs slightly less accurately but it is much faster than K + E.
• The larger the fold value, the more accurate the result of Modified K + E.
• Presence of missing data reduces the accuracy of K + E and Modified K + E by similar rates.

This paper considers cross-validation based approaches to automatically determine the appropriate number of dimensions to retain in a Principal Components Analysis (PCA). Three approaches based on a mixture of leaving groups of observations and variables out are described. They are compared through simulation across a range of datasets of differing sizes and differing levels of missingness using the NIPALS algorithm to carry out the PCA. Also included in the paper is an explicit description of how the NIPALS algorithm is implemented to deal with missing data. Finally we provide suggestions as to which approach offers a better compromise between reliability in choosing the optimal number of components, and the computational burden.