Rank selection in noist PCA with sure and random matrix theory

Principal component analysis (PCA) is probably the best known method for dimensionality reduction. Perhaps the most important problem in PCA is to determine the number of principal components in a given data set, and in effect separate signal from noise in the data set. Many methods have been proposed to deal with this problem but almost all of them fail in the important practical case when the number of observations is comparable to the number of variables, i.e., the realm of random matrix theory (RMT). In this paper, we propose to use Stein´s unbiased risk estimator (SURE) to estimate, with some assistance from RMT, the number of principal components. The method is applied on simulated data and compared to BIC and the Laplace method.