Reconstruction and RMS

Still working trying to get a protocol with R in a Notebook to detect adulteration or bad manufactured batches of a mixture.

It is important in the reconstruction the selection of the number of principal components. We get two matrices: T and P to reconstruct all the samples in the training set, so if we subtract from the real spectrum the reconstruction we get the residual spectrum.

These residual spectra may have information so we need to continue adding Principal Component terms until no information seems to be on them.
With new spectra batches we can project them on the PC space using the P matrix and get also their reconstructed spectra, and their residual spectra hoping to find patterns in the residual spectra which justify if they are bad batches.

This is the case of some of this batches shown in red over the blue residuals from the training data:

One way to measure the noise and to decide if the samples in red are bad batches respect the training samples is the statistic RMS. I overplot the RMS in blue for the training samples and in red for the test (in theory bad samples). The plot show that some of the test samples have higher RMS values than the training set.
A cutoff value can be fit in order to determine this in routine.