Empirical canonical correlation analysis in subspaces

• Published in: 2004 38th Asilomar Conference on Signals, Systems and Computers Vol. 1; pp. 994 - 997 Vol.1
• Main Authors: Pezeshki, A., Scharf, L.L., Azimi-Sadjadi, M.R., Lundberg, M.
• Format: Conference Proceeding
• Language: English
• Published: Piscataway NJ IEEE 2004
• Subjects: Applied sciences; Contracts; Covariance matrix; Data analysis; Detection, estimation, filtering, equalization, prediction; Estimation theory; Exact sciences and technology; Extraterrestrial measurements; Hilbert space; Information, signal and communications theory; Random variables; Signal and communications theory; Signal Processing; Signal, noise; Signalbehandling; State estimation; Statistical analysis; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Vectors; Canonical analysis; Parameter estimation; Covariance; Correlation analysis; Channel estimation; Two channel system; Transmission channel; Subspace method; Data transmission; Random variable; Canonical correlation
• ISBN: 0780386221; 9780780386228
• DOI: 10.1109/ACSSC.2004.1399288

This paper addresses canonical correlation analysis of two-channel data, when channel covariances are estimated from a limited number of samples, and are not necessarily full-rank. We show that empirical canonical correlations measure the cosines of the principal angles between the row spaces of the data matrices for the two channels. When the number of samples is smaller than the sum of the ranks of the two data matrices, some of the empirical canonical correlations become one, regardless of the two-channel model that generates the samples. In such cases, the empirical canonical correlations may not be used as estimates of correlation between random variables.