Re: [S] Canonical correlation analysis for prediction?

From: Renaud Lancelot (
Date: Mon Jan 18 1999 - 22:02:35 MET


I am not a specialist but there is a place to ask this question, which
is a discussion list specially devoted to multivariate data analysis: to join the list and to ask the question

you will find all the details at the web site (see there how to join the list)

and there is a FREE gorgeous software (in English !!!) with a huge
documentation, datasets and analysed examples. However, it's a whole
world and analysis are not always that simple...

Moreover, these people do like S-Plus !...

Hope this helps,


John Balding a écrit :
> The questions I have are only loosely related to S-PLUS, but since I am
> using S-PLUS (4.5R2 for win95) to do the work I thought this might be a
> good place to ask anyways. Answers on this list tend also to be much
> more helpful than those on the statistics newsgroups!
> I've been left to figure out a consultant's report commissioned in the
> early eighties. This report dealt with the prediction of levels of a
> number of stream pollutants from measures of discharge, rainfall, and
> other climate variables. Among the techniques employed was canonical
> correlation analysis. Because the audience was originally
> semi-technical, none of the equations were outlined in the report;
> unfortunately the person who authored the report has since passed away.
> I am left with the task of trying to see which of the techniques in the
> report might be valid for data from a number of watersheds we've since
> started monitoring. As luck would have it, I have almost no experience
> with CCA at all (although the other methods were relatively easy to
> understand).
> Both predictors and predictands were preprocessed using PCA and the
> resulting standardized scores used in the CCA. The CCA was performed on
> the correlation matrices, not the covariance matrices as seems to be the
> default in the S-PLUS cancor() routine. Because of my newness to CCA I
> decided to work through an example in Green's Analyzing Multivariate
> Data before tackling the report. I think I now have a basic grasp of the
> technique and roughly know what each of the resulting matrices means...
> unfortunately I can't figure out how one goes about predicting values of
> the predictands from new values of the predictors. What is the matrix
> equation for doing this?
> I have
> 1) the standardized predictor and predictand variables Xs and Ys
> (arranged in columns)
> 2) the correlation matrices Rxx, Ryy, Rxy, and Ryx
> 3) the matrix product F = Rxx^-1 Rxy Ryy^-1 Ryx
> 4) the diagonal matrix of eigenvalues D and the eigenvectors V of F
> 5) the diagonal matrix of canonical correlations M (ie. D^0.5)
> 6) the canonical weights matrices A and B (scaled such that A' Ryy A =
> I, and B' Rxx B = I)
> 7) the canonical loadings G = Ryy A and H = Rxx B
> 8) the canonical variate scores T = Ys A and U = Xs B
> Now how do I get from Xs(new) to Ys(new)? I would also like to be able
> to select the number of canonical variates to be used in the final
> prediction equation (much like selecting the number of PCs to use, I
> would assume). I know there must be a very simple matrix equation for
> predicting values of the predictands from values of the predictors using
> the results of CCA. I just need a little help!
> Thank you very much,
> John
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Renaud Lancelot
BP 2057 Dakar-Hann
tel (00 221) 832 49 02 work
    (00 221) 824 57 12 home
fax (00 221) 821 18 79 (CIRAD)

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