Residual Variance

We´ve been talking about how to use the PCs, and how to reconstruct the original spectrum from its PC scores and the eigenvectors. After this we compared the reconstructed spectrum to the original one to get a residual value:

Residual (R) = Spectrum _original – Spectrum _{reconstructed}

If the PCs space represent the 100% of the variance of the training set, then the residual would be zero for the training set samples, but this is not the case.

The variance for the residual spectrum is:

Vr = R^T.R

This variance can be used as an indicator if a sample belongs to a spectra population. This is the method known as “Residual Variance”.