Random Subspace Analysis on Canonical Correlation of High Dimensional Data

Abstract: High dimensional, low sample, data have singular sample covariance matrices,rendering them impossible to analyse by regular canonical correlation (CC). Byusing random subspace method (RSM) calculation of canonical correlation be-comes possible, and a Monte Carlo analysis shows resulting maximal CC canreliably distinguish between data with true correlation (above 0.5) and with-out. Statistics gathered from RSMCCA can be used to model true populationcorrelation by beta regression, given certain characteristic of data set. RSM-CCA applied on real biological data however show that the method can besensitive to deviation from normality and high degrees of multi-collinearity.