---
_id: '40870'
abstract:
- lang: eng
text: The assessment of multivariate association between two complex random vectors
is considered. A number of correlation coefficients based on three popular correlation
analysis techniques, namely canonical correlation analysis, multivariate linear
regression, and partial least squares, are reviewed and connected to performance
measures in signal processing and communications, such as mean-squared estimation
error, mutual information, and signal-to-noise ratio (SNR). For complex data,
there are three types of correlation coefficients, which account for rotational,
reflectional, and total (i.e., rotational and reflectional) dependencies between
two random vectors. These three types are defined and analyzed for different correlation
coefficients, and a numerical example is given. It is often required to compare
two complex random vectors in a lower-dimensional subspace. For the large class
of increasing, Schur-convex correlation coefficients, it is shown that the low-rank
approximations of two random vectors maximizing a particular correlation coefficient
are determined only by the constraints imposed on the correlation analysis technique.
In this context, the correlation spread is defined as a normalized measure of
how much of the overall correlation is contained in a low-dimensional subspace.
author:
- first_name: Peter J.
full_name: Schreier, Peter J.
last_name: Schreier
citation:
ama: Schreier PJ. A Unifying Discussion of Correlation Analysis for Complex Random
Vectors. *{IEEE} {T}rans\ {S}ignal\ {P}rocess*. 2008;56(4):1327–1336. doi:10.1109/TSP.2007.909054
apa: Schreier, P. J. (2008). A Unifying Discussion of Correlation Analysis for Complex
Random Vectors. *{IEEE} {T}rans.\ {S}ignal\ {P}rocess.*, *56*(4), 1327–1336.
https://doi.org/10.1109/TSP.2007.909054
bibtex: '@article{Schreier_2008, title={A Unifying Discussion of Correlation Analysis
for Complex Random Vectors}, volume={56}, DOI={10.1109/TSP.2007.909054},
number={4}, journal={{IEEE} {T}rans.\ {S}ignal\ {P}rocess.}, author={Schreier,
Peter J.}, year={2008}, pages={1327–1336} }'
chicago: 'Schreier, Peter J. “A Unifying Discussion of Correlation Analysis for
Complex Random Vectors.” *{IEEE} {T}rans.\ {S}ignal\ {P}rocess.* 56, no.
4 (2008): 1327–1336. https://doi.org/10.1109/TSP.2007.909054.'
ieee: 'P. J. Schreier, “A Unifying Discussion of Correlation Analysis for Complex
Random Vectors,” *{IEEE} {T}rans.\ {S}ignal\ {P}rocess.*, vol. 56, no. 4,
pp. 1327–1336, 2008, doi: 10.1109/TSP.2007.909054.'
mla: Schreier, Peter J. “A Unifying Discussion of Correlation Analysis for Complex
Random Vectors.” *{IEEE} {T}rans.\ {S}ignal\ {P}rocess.*, vol. 56, no. 4,
2008, pp. 1327–1336, doi:10.1109/TSP.2007.909054.
short: P.J. Schreier, {IEEE} {T}rans.\ {S}ignal\ {P}rocess. 56 (2008) 1327–1336.
date_created: 2023-01-30T11:52:04Z
date_updated: 2023-01-30T11:56:07Z
department:
- _id: '263'
doi: 10.1109/TSP.2007.909054
intvolume: ' 56'
issue: '4'
page: 1327–1336
publication: '{IEEE} {T}rans.\ {S}ignal\ {P}rocess.'
status: public
title: A Unifying Discussion of Correlation Analysis for Complex Random Vectors
type: journal_article
user_id: '43497'
volume: 56
year: '2008'
...