Subtracting spectra to understand band positions

In this exercise (with the soy meal data in transmittance), we sort the soy meal spectra in four data-frames, by protein, moisture, fat and fiber, so in the first row we have the spectrum absorbance of the sample with the minimum value of protein, moisture, fat and fiber, and in the last one the sample with the maximum.

 

After, we subtract the spectra of the maximum and minimum to get the difference spectrum. Sometimes ,this spectrum difference help us to understand where are the main bands for the main constituents.

 

In this case is not easy due that we are working in a zone where the bands are very wide (second and third overtones), and the math treatment does not remove that overlapping (MSC). Anyway we can see some curiosities.

In the plots we see the minimum and maximum spectrum and the difference spectrum. In the next plot I overlap the difference spectra:

We have to take into account that we still have the interferences of the moisture (as example) over the other bands due that the high  range (when the spectra is sorted) is for the constituent sorted, but there are range for the other constituents. Anyway seems to be more or less clear where are the absorbance bands in this NIT zone for protein and moisture.

As a curiosity, see how the Fiber difference spectrum is the opposite than the Protein difference spectrum due to the negative correlation between these two constituents for the soy meal.

 

All the plots are outputs of "R" code.

 

Abstracts ready for Eleventh Winter Symposium on Chemometrics (WSC)

Abstracts for the presentations of the  Eleventh Winter Symposium on Chemometrics (WSC) are ready to be consult on the WSC web page. A lot of readers of this blog are from Russia, and I would like to say thanks to all from here.

Std Dev vs. Mean Centered Spectrum

This is a plot which shows the mean centered spectra treated with Multiple Scatter Correction, and over plotted is the estándar deviation values of the mean centered values at each wavelength.
The idea is to create a plot with different scales and laves in the axes, and the result is quite nice with this code:
## Plotting the Standard Deviation Spectrum
X_msc_mc_sd<-as.matrix(apply(X_msc_mc,2,sd))
par(mar=c(5, 4, 4, 6))
matplot(wavelengths,t(X_msc_mc),type="l",col="grey",
        xlab="",ylab="",axes=FALSE)
mtext("Absorbancia",side=4,col="grey",line=3)
axis(4,col="grey",col.axis="grey",las=1)
par(new=TRUE)
matplot(wavelengths,X_msc_mc_sd,lty=1,pch=NULL,axes=FALSE,
        type="l",col="red",lwd=2,xlab="Wavelength",ylab="",
        main= "Std Dev vs Mean centered spectra")
axis(2,col="red",col.axis="red",las=1)
mtext("Standard Deviation",col="red",side=2,line=3)
axis(1,col="black",col.axis="black",las=1)
box()

Practice with this example.

RStudio Tips and Tricks

If you use R there are videos and tutorials which can help you to improve your work, so I will add some of them  in the blog, under the label VIDEO: R-Tutorials 

Correlation between scores and PC / PLS terms

First PC search to explain the maximum variability in the X matrix. Once extracted the second PC explain the maximum variance remaining, and the process is repeated until almost all the important variance is explained and the remaining variance is the noise and we don´t want it to incorporate this variance into the model.

Once we have the terms, samples are projected over the several PC terms and every sample has a score for every term. Therefore, we have a score matrix with “N” samples (rows) and “A” components (columns).

This variance can be due to different sources or mixture of sources.

In the case of PLS we are looking for a compromise explaining the maximum possible variance in X, at the same time that we explain a maximum variance in Y. We have also a score matrix when developing the PLS algorithm and this scores have more correlation with the constituent that the scores calculated with PC.

In the case of the soy meal in the conveyor, we can calculate the correlation between the scores for every  of the four PC and the protein:

> cor(scores_4t_pc[,1:4],soy_ift_prot1r1$Prot)

               [,1]

PC term 1  -0.2105997
PC term 2   0.3445256
PC term 3   0.1647146
PC term 4  -0.6888083

We can do the same, but with the scores of the PLS regression:

> cor(Prot_plsr_r1$scores[,1:4],soy_ift_prot1r1$Prot)

            [,1]

Comp 1 0.2129742
Comp 2 0.4193727
Comp 3 0.5348858
Comp 4 0.4425912

As I can see the correlations are higher for the PLS, but there are some curiosities about the PC scores that we can try to check yin future posts.