Generalized canonical correlation

<h2 id="applications">Applications</h2>
<p>The <a href="/facts/Helmert-Wolf_blocking/v5u664nB">Helmert-Wolf blocking</a> (HWB) method of estimating <a href="/facts/Linear_regression/5n998IhK">linear regression</a> parameters can find an optimal solution only if all cross-correlations between the data blocks are zero. They can always be made to vanish by introducing a new regression parameter for each common factor. The gCCA method can be used for finding those harmful common factors that create cross-correlation between the blocks. However, no optimal HWB solution exists if the random variables do not contain enough information on all of the new regression parameters.
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<ul><li>Afshin-Pour, B.; Hossein-Zadeh, G.A. Strother, S.C.; Soltanian-Zadeh, H. (2012), <a href="http://www.sciencedirect.com/science/article/pii/S1053811912001644">"Enhancing reproducibility of fMRI statistical maps using generalized canonical correlation analysis in NPAIRS framework"</a>, NeuroImage 60(4): 1970–1981. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.neuroimage.2012.01.137">10.1016/j.neuroimage.2012.01.137</a></li>
<li>Sun, Q.S., Liu, Z.D., Heng, P.A., Xia, D.S. (2005) "A Theorem on the Generalized Canonical Projective Vectors". <i>Pattern Recognition</i> 38 (3) 449</li>
<li>Kettenring, J. R. (1971) "Canonical analysis of several sets of variables". "Biometrika" 58 (3) 433</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="http://factominer.free.fr/">FactoMineR</a> (free exploratory multivariate data analysis software linked to <a href="/facts/R_programming_language/LSrkr8K8">R</a>)</li></ul>

Generalized canonical correlation open-in-new

Generalized canonical correlation