Re: Principal Components (Hotelling of KL Transform) of 2 Band (Red and Green) Real Color Image

PeterOut wrote:
On Jan 6, 5:37 am, Jonathan Campbell <jg.campbell...@xxxxxxxxx> wrote:
PeterOut wrote:
Say you have a 2 channel image (red and green channels for example)
and you want to get the principal components in order to do a
Hotelling (Karhunen-Loève) transform on the image so as to minimize
[...]
Thank you very much for your reply. You are right. I checked and it
would appear that it is indeed the covariance matrix that I should
use. However, it would appear that I would have the same problem
since covariance is reflective and, consequently, the covariance
matrix between the two data sets would be

M=1 a
a 1


Not unless the variance of both channels is 1? As I say, I have never applied PCA/K-L to 2-d. data, so I'm a little hesitant.

Variance-covariance matrix = Cov = E{ (x - mu) (x - mu)^T } ? 2 x 2 in your case. mu = mean.

You know the usual tutorial example on PCA (I think if you search newsgroups like this one and comp.ai.neural-nets, you'll find similar written by me): 2-d. data set ... scatter plot showing ellipse shaped cloud with the major axis aligned along the diagonal (0.707, 0.707)? The conventional wisdom days that the first eigenvalue will be the variance along that diagonal axis and the first eigenvector along that diagonal.

I'm trying to think how the shape of the cloud depends on your 'a', but I'm not getting too far.

What does your scatter plot (original data) look like?

Best regards,

Jon C.
.