Automatic Choice of Dimensionality for PCA

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 k-frames, which is di cult to compute exactly. But after choosing an appropriate parameterization and applying Laplace's method, an accurate and practical estimator is obtained. In simulations, it is more accurate than cross-validation and other proposed algorithms, plus it runs much faster.

• Type: Conference
• Year: 2000
• Where: NIPS
• Authors: Thomas P. Minka
• Keywords: Bayesian Model Selection, NIPS 2000, NIPS 2007, Principal Component Analysis, Principal Components