Thomas P. Minka

Abstract

A central issue in principal component analysis
PCA is choosing the number of principal components to be retained By interpreting PCA as density estimation this paper shows how to use Bayesian model selection to determine the true dimensionality of the data The resulting estimate is simple to compute yet guaranteed to pick the correct dimensionality given enough data The estimate involves an integral over the Steifel manifold of kframes which is dicult to compute exactly But after choosing an appropriate parameterization and applying Laplaces method an accurate and practical estimator is obtained In simulations it is more accurate than crossvalidation and other proposed algorithms plus it runs much faster
Intr