PCA for NIR Spectra_part 005: "Reconstruction"

February 27, 2012

(This article was first published on NIR-Quimiometría, and kindly contributed to R-bloggers)

We saw how to plot the raw spectra (X), how to calculate the mean spectrum, how to center the sprectra (subtracting the mean spectrum from every spectra of the original matrix X). After that we have developed the PCAs with the NIPALS algorithm, getting two matrices: T (scores) and P (loadings).
We have to decide the number of PCs, looking to the plots, or to the numbers (explained variance).
Depending of the numbers of PCs, these matrices will have more or less columns.
With these two matrices we can reconstruct again the X centered matrix, but we´ll get also a residual matrix “E”.
Xc = T.Pt+E

This post just shows this in R:

> P3pc_nipals<-P_nipals[,1:3]
> tP3pc_nipals<-t(P3pc_nipals)
> Xc3pc_reconst<-T3pc_nipals
> Xc3pc_reconst<-T3pc_nipals%*%tP3pc_nipals
> matplot(wavelengths,t(Xc3pc_reconst),lty=1,
  + pch=1,xlab=”data_points”,ylab=”log(1/R)”)
> resid3pc<-Xc- Xc3pc_reconst
> matplot(wavelengths,t(resid3pc),lty=1,
  + pch=1,xlab=”data_points”,ylab=”log(1/R)”)

We can see the plots of the X centered matrix reconstructed and the plot representing the residual variance or Error matrix “E”. If we add the mean spectrum to every spectra of the centered matrix we will get the X matrix reconstructed.

To leave a comment for the author, please follow the link and comment on their blog: NIR-Quimiometría.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...


Comments are closed.

Search R-bloggers


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)