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res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Peter J.
foaf_name: Schreier, Peter J.
foaf_surname: Schreier
bibo_doi: 10.1109/TSP.2007.909054
bibo_issue: '4'
bibo_volume: 56
dct_date: 2008^xs_gYear
dct_title: A Unifying Discussion of Correlation Analysis for Complex Random Vectors@
...