## 19 may. 2013

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

Using NIPALS algorithm for PCA, I get two objects:
T : score 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.

#### 2 comentarios:

1. Congrats for the post, José Ramón. The level is increasing...

1. Thanks a lot Antonio.
Best Regards