21 de abr. de 2012

R^2 Spectrum

We have seen in the previous post, how to calculate the correlation spectrum, but other simple way to show  how the bands correlate to the constituent of interest is to calculate R^2. This way we remove the negative part of the correlation spectrum.
Xmsc<-NIR_msc
Ymoi<-demo_raw$Moisture
cor_spec<-cor(Ymoi,Xmsc[,1:700])
rsq_spec<-(cor(Ymoi,Xmsc[,1:700]))^2
cov_spec<-cov(Ymoi,Xmsc[,1:700])*50
matplot(wave_nir,t(cor_spec),lty=1,pch="*",xlab="nm",ylab="log(1/R)")
matplot(wave_nir,t(rsq_spec),lty=1,pch="*",xlab="nm",ylab="log(1/R)")
matplot(wave_nir,t(cov_spec),lty=1,pch="*",xlab="nm",ylab="log(1/R)")
#We merge the R /R^2/Cov spectrum with the sample spectra treated with MSC.
cor_spec<-rbind(cor_spec,NIR_msc)
rsq_spec<-rbind(rsq_spec,NIR_msc)
cov_spec<-rbind(cov_spec,NIR_msc)
matplot(wave_nir,t(cor_spec),lty=1,pch="*",xlab="nm",ylab="log(1/R)")
matplot(wave_nir,t(rsq_spec),lty=1,pch="*",xlab="nm",ylab="log(1/R)")
matplot(wave_nir,t(cov_spec),lty=1,pch="*",xlab="nm",ylab="log(1/R)")

In order to see better the Covariance Spectrum, I multiplied by a factor,We can see how the covariance spectrum gives sharp bands an gives us a better idea where the variation due to moisture is.

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