How do your NIR measurements compare with reference methods?

How do your NIR measurements compare with reference methods?

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Mahalanobis: "This time with the NIPALS " T " matrix"

Using NIPALS algorithm for PCA, I get two objects:
T : score matrix
P : loadings matrix
library(chemometrics)
sflw.msc3.tra_nipals<-nipals(sflw.msc3.tra$NIRmsc,a=10,it=160)
"sflw.msc3.tra$NIRmsc" is my training set spectra treated with MSC.
names(sflw.msc3.tra_nipals)
[1] "T" "P"
dim(sflw.msc3.tra_nipals$T)
#T matrix dimension (n . p)
[1] 107  10
n = number of samples
p = number of PCs
dim(sflw.msc3.tra_nipals$P)
#P matrix dimension (m . p)
[1] 2800   10
m = number of wavelengths
p = number of PCs

Let´s use the drawMahal (classical) function in this case in the T matrix:
T_nipals<-sflw.msc3.tra_nipals$T
Xn.pc1pc2<-T_nipals[,1:2]
Xn.pc1pc3<-T_nipals[,c(1,3)] 
Xn.pc1pc4<-T_nipals[,c(1,4)]
Xn.pc2pc3<-T_nipals[,c(2,3)]
Xn.pc2pc4<-T_nipals[,c(2,4)]
Xn.pc3pc4<-T_nipals[,c(3,4)]   
par(mfrow=c(2,3))
drawMahal(Xn.pc1pc2,center=apply(Xn.pc1pc2,2,mean),
            covariance=cov(Xn.pc1pc2),quantile=0.975)
drawMahal(Xn.pc1pc3,center=apply(Xn.pc1pc3,2,mean),
            covariance=cov(Xn.pc1pc3),quantile=0.975)
drawMahal(Xn.pc1pc4,center=apply(Xn.pc1pc4,2,mean),
            covariance=cov(Xn.pc1pc4),quantile=0.975)
drawMahal(Xn.pc2pc3,center=apply(Xn.pc2pc3,2,mean),
            covariance=cov(Xn.pc2pc3),quantile=0.975)
drawMahal(Xn.pc2pc4,center=apply(Xn.pc2pc4,2,mean),
            covariance=cov(Xn.pc2pc4),quantile=0.975)
drawMahal(Xn.pc3pc4,center=apply(Xn.pc3pc4,2,mean),
            covariance=cov(Xn.pc3pc4),quantile=0.975)

 

To understand better these plots we can have a look to the P (loadings) matrix:

 P_nipals<-sflw.msc3.tra_nipals$P
par(mfrow=c(2,2))
matplot(data.points,P_nipals[,1],type="l",lty=1,xlab="nm",
        ylab="log 1/R")
matplot(data.points,P_nipals[,2],type="l",lty=1,xlab="nm",
        ylab="log 1/R",col="blue")
matplot(data.points,P_nipals[,3],type="l",lty=1,xlab="nm",
        ylab="log 1/R",col="green")
matplot(data.points,P_nipals[,4],type="l",lty=1,xlab="nm",
        ylab="log 1/R",col="brown")
 

 

Looking to the loading plots we can have an idea of which type of variability the loading is representing. In the first and the second (specially in the first one we can see some bands related to the water and fat.

 

 

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Robust Mahalanobis Ellipse

In this plot we compare the Mahalanobis ellipse, using as center, the mean of the columns and as covariance, the classical covariance (is the same plot than in the previous post, but in this case I added colors and symbols to the samples, according to their sample set), and the Mahalanobis ellipse, based on the robust statistics (in this case the Minimum Covariance Determinant).

The calculation of the MCD is done with the function: covMcd( ). This function gives new robust values: center and cov to use indeed the classical ones.

We see how the distribution of the samples, in the ellipse, change, and also the number of outliers detected.