Canonical.txt
Thanks to all who responded to my query regarding the "canonical" in
"canonical correlation/regression." Here is a summary (excerpts) of the
replies I have received.
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Sun, 04 Jun 95 11:03:32 EDT
From: "Karl L. Wuensch"
Subject: CANONICAL correlation/regression
To: Multiple recipients of list
Why is a "canonical correlation/regression" referred to as "canonical?"
I was asked this by one of my students a few days ago and was unable to find
an answer to it.
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From: Mark Eakin
For whatever its worth, Webster's New Collegiate Dictionary (1981) on page
160-161 defines canonical as:
"5. reduced to the simplest or clearest schema possible"
Of course the same dictionary defines the mean as midway between extremes
(the midrange) before it defines it as the average of values.
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From: hthomp2@lsumc.edu (Hilary Thompson Ph.D.)
My microsoft bookshelf dictionary's third meaning in the definition of
canonical is "conforming to orthodox rules". I suspect this meaning is the
one important in the derivation of the use of canonical in this sort of
analysis since it involves the generation of linear combinations of
variables, one linear combination from two sets of variates, with this
pairing continuing until all variance is accounted for by pairs of linear
combinations. Both the linearity and the total accounting for variance
"conforming to orthodox rules".
It might be interersting to look at the references which are often cited
as the origin of canonical analysis:
Hotelling, H 1935. The most predictable criterion. Journal of Educational
Psychology. 26:139-142.
Hoteling, H 1936. Relations between two sets of variates. Biometrika 28:321-377.
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From: J.M.Bibby@shu.ac.uk (JOHN BIBBY)
"Canonical" just means "standard", and "Canonical forms" are
representations of matrices in terms of their Canonical vectors
(eigen-vectors).
What would be better terminology for Canonical correlation? It's just
"regression with many dependent variables". Let me know what you decide!
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From: Jon_Richards@nbs.gov
Good question! I thought, "I know that, it is... uhh...". So I went
to Websters 3rd International Dictionary, Unabridged (of English ;-)
and found a definition "5. relating to various of the simplest and
most significant forms or schemata to which general equations,
statements, or expressions may be reduced without loss of generality."
It then provides an example "the canonical equations of dynamics",
which leads my mind back to physics. As in the canonical form of
Maxwell's equations, which are a set of differential equations which
may be manipulated, depending on bounding conditions, to solve for
electromagnetic radiation.
I guess whoever came up with canonical correlation/regresssion/...
must have thought s/he was reducing the data to a simpler form or
scheme?