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.