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I came across the article by Hervé Abdi about generalized SVD. The author mentioned:

The generalized SVD (GSVD) decomposes a rectangular matrix and takes into account constraints imposed on the rows and the columns of the matrix. The GSVD gives a weighted generalized least square estimate of a given matrix by a lower rank matrix and therefore, with an adequate choice of the constraints, the GSVD implements all linear multivariate techniques (e.g., canonical correlation, linear discriminant analysis, correspondence analysis, PLS-regression).

I'm wondering how the GSVD is related to all linear multivariate techniques (e.g., canonical correlation, linear discriminant analysis, correspondence analysis, PLS-regression).

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Section 4.1 of the article describes what the matrices, M and W, have to be for the generalized SVD to yield results comparable to correspondence analysis. The author also cites his reference #3 to explain how the generalized SVD can yield results comparable to the other multivariate methods mentioned.

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    $\begingroup$ I have bookmarked this question very long ago. I would be very interested to see a clear and self-contained answer that might serve as a reference in the future. Do you think you can make it? $\endgroup$ – chl Jul 28 '12 at 20:26

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