PCA with the first derivative

In a previous post we had calculated the PCA with the math treatment SNV+Detrend and we calculated a first sample set of outliers with the Mahalanobis distance. 

When calculating PCA we have to treat as best the spectra as possible in order to detect populations or boundaries and if we treat the spectra with math treatments which help to do this task is great. So indeed, to apply the SNV + Detrend, I apply this time the first derivative to the spectra (soil from Spanish soil from LUCAS database) and calculate the PCA.

We can have a look to the score’s maps (six PC recommended) to find if there are boundaries on them:

Look at the maps which include PC2 as one of the axes. There are a certain number of samples which takes a different direction than the rest. This second PC term can be useful to find something interesting on the spectra.

 To see what is happening we can see the loading spectra for this second PC term:

This loading spectra has the first derivative math treatment applied, so we can compare it with a library of reference known spectra (minerals in this case) to see which is the best match, and in this case the best match is with the gypsum mineral, so this second term is explaining part of the variance included in our spectra database due to the addition of gypsum to the soil.