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Physicist here. I have a dataset. The data is the emission from a molecule that has two dipoles. Molecules can only emit along these dipoles.

As I rotate the molecule, I will selectively excite the dipoles, thus my gaussian emission should change and become squished and more ellipsoid. And it does!

e.g squished gaussian emission

enter image description here

Now, I was hoping to do some PCA (principal component analysis) and I should get two principal components which would've changed as the direction of the emission changes and correspond to the dipoles. (i.e. two component eigenvalues which make up all the emission), see this image from wikipedia

enter image description here

However, when I've done PCA I've always done it on individual data points (think scatter plot)- "coordinate like" data points. But my data is really the total number of counts on each pixel, not individual points on a graph. The data looks like a matrix like:

(0,0,0.5,0,0) 
(0,0.5,1,0.5,0) 
(0,0.5,1,0.5,0) 
(0,0,0.5,0,0) 

where the numbers correspond to the level of emission from that point. I could create a number datapoints which correspond to the intensity at pixel.

I feel that it is dodgy to infer the individual counts from a total count. The mapping between sums and their constituents is not bijective.

So, Can I still use PCA in this scenario? Is there a better method?

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  • $\begingroup$ It's possible to fit a Gaussian distribution to the total counts, then diagonalize the covariance matrix to find the directions of maximum variance. Are you asking how to do this? Or, are you asking whether it would be valid? In the latter case, I think we might need more details to better understand the data generating process, and the goals/assumptions of your analysis (i.e. what counts as valid). $\endgroup$ – user20160 Mar 9 at 20:47

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