Canonical correlation analysis of high-dimensional data with very small sample support

•A technique to determine the number of correlated signals between two data sets is proposed.•Based on a combination of principal component analysis and canonical correlation analysis.•The technique works for extremely small number of samples.•Very simple yet effective approach.

This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the data. In such a scenario, a principal component analysis (PCA) rank-reduction preprocessing step is commonly performed before applying canonical correlation analysis (CCA). We present simple, yet very effective, approaches to the joint model-order selection of the number of dimensions that should be retained through the PCA step and the number of correlated signals. These approaches are based on reduced-rank versions of the Bartlett–Lawley hypothesis test and the minimum description length information-theoretic criterion. Simulation results show that the techniques perform well for very small sample sizes even in colored noise.