PCA Subtract Channel Means

[e-koch]

Normalization for PCA is by column of data. Mean subtraction should be by channel instead of the whole cube.

[low-sky]

:+1:

See also new PCA

[e-koch]

Also, should be dividing by N-1 instead of N for the sample covariance. The difference will matter for channels with only a few non-noisy pixels, not so much the others.

[low-sky]

@e-koch -- Note that the Brunt & Heyer PCA implementation does no mean subtraction in calculation of the data. Bessel's correction wouldn't apply then, would it? I'm still testing this in cloudpca

[e-koch]

@low-sky They subtract it in the original paper, but don't use Bessel's correction for the covariance. In the 2013 paper I guess it is assumed? I don't think the output can be called PCs if the channels aren't mean subtracted. It won't be the covariance matrix that's computed.

[low-sky]

@e-koch That's fair. I'm going to see how it changes things. The claim in Brunt & Heyer (2003) is that it only shows up in the outer scale, which is what's important for the first eigenvalue and the size / line-width used in Dario's work.

[e-koch]

Addressed in #35 , #36.