PCA STABILITY AND CHOICE OF DIMENSIONALITY

A Criterion of stability for PCA scatterplots is defined based on a classical distance between projectors. It is constructed as a risk function and can be estimated by bootstrap or jackknife methods. Furthermore, perturbation theory is used to write down a Taylor expansion of the jackknife estimate for reasons of computational cost and in order to obtain an analytic expression for the approximation. The comparative study of these three estimates on real data shows that the last one is easy to compute, sufficiently accurate and helpful in choosing dimensionality in PCA.