Problem with random variables in Matlab's PCA

[confused_engineer]

TL;DR Summary

I cannot calculate the random variables associated to the eigenfuctions of the principal component analysis.

Hello.

I have designed a Gaussian kernel as:

[X,Y] = meshgrid(0:0.002:1,0:0.002:1);
Z=exp((-1)*abs(X-Y));

Now, I calculate PCA:

[coeffG, scoreG, latentG, tsquaredG, explainedG, muG]=pca(Z, 'Centered',false);

I can rebuid the original data propperly as defined in the dcumentation https://la.mathworks.com/help/stats/pca.html#bth9ibe-coeff:

Zrec=scoreG*coeffG';

Now, I wish to calculate the uncorrelated random variables which acompany the eigenvectors, columns of scoreG. For that, I do the following:

randvarG=Z*scoreG(:,1); However, the resulting histogram of randvarG does not look gaussian at all.

Any hindsight on what I am doing wrong is very appreciated.
Thanks for reading

 

[NateD]

.In order to calculate the uncorrelated random variables that accompany the eigenvectors, you need to transform the data using the eigenvectors. This is done by multiplying the original data matrix (Z) with the transposed eigenvectors matrix (coeffG'). The resulting matrix is then used to calculate the uncorrelated random variables. For example, you can use the following code to calculate the uncorrelated random variables:transformedData = Z*coeffG';randvarG=transformedData(:,1);This should give you the expected Gaussian histogram.