Citation:
Song, Y., Schreier, P. J., Ramírez, D., & Hasija, T. (2016). Canonical correlation analysis of high-dimensional data with very small sample support. Signal Processing, 128, 449-458
xmlui.dri2xhtml.METS-1.0.item-contributor-funder:
Ministerio de Economía y Competitividad (España) Comunidad de Madrid
Sponsor:
This research was supported by the German Research Foun-dation (DFG) under grant SCHR 1384/3-1, and the Alfried Kruppvon Bohlen und Halbach foundation under its program “Return ofGerman scientists from abroad”. The work of D. Ramírez has been partly supported by Ministerio de Economía of Spain under projects: COMPREHENSION (TEC2012-38883-C02-01), OTOSIS(TEC2013-41718-R), and the COMONSENS Network (TEC2015-69648-REDC), by the Ministerio de Economía of Spain jointly withthe European Commission (ERDF) under project ADVENTURE(TEC2015-69868-C2-1-R), and by the Comunidad de Madrid under project CASI-CAM-CM (S2013/ICE-2845).
Project:
Gobierno de España. TEC2012-38883-C02-01 Gobierno de España. TEC2013-41718-R Gobierno de España. TEC2015-69648-REDC Gobierno de España. TEC2015-69868-C2-1-R Comunidad de Madrid. S2013/ICE-2845
Keywords:
Bartlett-Lawley statistic
,
Canonical correlation analysis
,
Model-order selection
,
Principal component analysis
,
Small sample support
,
Information-theoretic criteria
,
Signals
,
Noise
,
Number
,
Components
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 scenaThis 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.[+][-]