Determining the number of correlated signals between two data sets using PCA-CCA when sample support is extremely small

This paper is concerned with determining the number of correlated signals between two data sets when the number of samples from these data sets is extremely small. In such a scenario, a principal component analysis (PCA) preprocessing step is commonly performed before applying canonical correlation analysis (CCA). We present a reduced-rank version of the hypothesis test based on the Bartlett-Lawley statistic, which allows jointly determining the required PCA dimension reduction and the number of correlated signals.