Canonical Correlation Analysis, reversiblity

Hello everyone,

I have little problem with the function canoncorr(...).

If I've understood correctly, the function returns two values a and b respecting a.X = b.Y.

So, if if I do:

[a,b] = canoncorr(X,Y)

I should get the same as:

[b,a] = canoncorr(Y,X)

But for some reason, when I have large matrices (I've actually seen this happen with 3*900 matrices), the results vary slightly.

Is this a problem of inaccuracy with matlab or do I need to brush up on my maths lessons?

Thank you lot for you answers

Answer 1

[Walter Roberson]

It is expected that the results would differ slightly, due to different order of operations.

Internally, the code computes two qr() independently -- that part should produce exactly the same results regardless of which order the matrices are.

But then the code does svd(Q1' * Q2,0) . It is to be expected that Q1' * Q2 differs slightly from Q2' * Q1 that you would get if the arrays were switched.

[Romain]

Thank you very much