A Corrected Criterion for Selecting the Optimum Number of Principal Components

Abstract

Determining the optimum number of components to be retained is a key problem in principal component analysis (PCA). Besides the rule of thumb estimates there exist several sophisticated methods for automatically selecting the dimensionality of the data. Based on the probabilistic PCA model Minka (2001) proposed an approximate Bayesian model selection criterion. In this paper we correct this criterion and present a modified version. We compare the novel criterion with various other approaches in a simulation study. Furthermore, we use it for finding the optimum number of principal components in hyper-spectral skin cancer images.