Model-order selection for analyzing correlation between two data sets using CCA with PCA preprocessing

This paper is concerned with determining the number of correlated signals between two data sets using canonical correlation analysis (CCA) when a principal component analysis (PCA) preprocessing step is performed for initial rank reduction. In signal processing applications, it is commonplace in scenarios with large dimensions, insufficient samples, or knowledge of low-rank underlying signals to extract the principal components of the data before correlation is analyzed. While there exist information-theoretic criteria to either determine the number of signals in a single data set or the number of correlated signals between two data sets, there has yet to be a treatment of the joint order estimation of the number of dimensions which should be retained through the PCA preprocessing and the number of correlated signals. We present the likelihood and information criteria for this scenario, along with some verifying simulations.