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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. (C) 2016 Elsevier B.V. All rights reserved.
bartlett-lawley statistic; canonical correlation analysis; model-order selection; principal component analysis; small sample support; information-theoretic criteria; signals; noise; number; components