NIPALS: Reconstruction of a Validation Set

In this post I calculate the scores of a validation set using the NIPALS loadings (Matrix P) calculated in the post: Using R: NIPALS Spectra Reconstruction

 

 Xval_orig<-scale(sflw.msc3.val$NIRmsc,center=TRUE,scale=FALSE)

matplot(wave.NIR,t(Xval_orig),type="l",lty=1,xlab="nm",

+ ylab="log 1/R")

 

Calculation of the scores is just a matrix multiplication of the centered validation matrix, by the P loadings matrix.

 

Tval_nipals<-Xval_orig %*% P_nipals

 

We have seen the loadings in the post: NIPALS: Correlation of the Scores with the Constituents

 

Now we can reconstruct the Xval with:

 Xval_recon<-Tval_nipals%*%(t(P_nipals))

matplot(wave.NIR,t(Xval_recon),type="l",lty=1,xlab="nm",

 + ylab="log 1/R")

Diference is the not explained variance, ramdon noise,....
 Eval<-Xval_orig-Xval_recon
matplot(wave.NIR,t(Eval),type="l",lty=1,xlab="nm",
+ ylab="log 1/R")