Peter J. Wahle <[EMAIL PROTECTED]> wrote:
> Thanks for the responses, but I'm not interested in merely checking each
> vector pair one at a time. I need to know the correlation between two sets
> of vectors. Each vector set can have hundreds or thousands of vectors, each
> set having the same number of vectors, and each corresponding vector have
> the same conditions. Perhaps my terminology is not quit correct.
> Experiment1 Experiment2
> Input1 (-1,1) (-2,-1)
> Input2 (-2,0) (-2,0)
> Input3 (-2,1) (-1,0)
> Input4 (0,0) (0,0)
> Input5 (-1,1) (-1,0)
> ... ... ...
> InputN (1,1) (1,1)
> The experiments output a 2D vector for each input condition. How can I
> calculate the correlation or dependence of these two experiments?
As others have said, look into canonical correlations. It's an
eigensystem method that finds the linear combination of components of each
set of vectors that has the maximum Pearson correlation, and then the
linear combination with the the next to maximum correlation and which is
orthogonal to the first, and so on, up to the dimension of the smaller
vector.
Linear regression is essentially canonical correlation where one of the
vectors has dimension one. Again the idea is to find the linear
combination of the components of the second vector that has the maximum
correlation with the first.
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