142
K. M. Sørensen et al.
reflectance at 2244 nm and the degree of esterification %DE is nearly perfect (R
2
=
0.99) albeit in opposite direction (second-derivative points peak downward).
When the pre-processing has been decided and when regression is the target, it is
often useful (but not so often supported by software packages) to plot a covarygram.
This is simply a plot of the correlation of the response value (%DE in Dataset 1) for
each spectral variable.
Figure 7.13 shows such a covarygram made on the MSC transformed spectra. It
immediately visualized that one dominant spectral variable, namely 2244 nm, has a
correlation coefficient of 1.0 to the reference variable %DE. The figure also shows
that large parts of the NIR spectrum contain data that are uncorrelated to the %DE
and therefore can (in principle) be excluded in a multivariate regression model. This
will be further discussed in the variable selection subchapter.
As computers are getting faster and chemometric software packages more and
more complete, most if not all, relevant pre-processing methods will be present in
the software packages. It is sometimes even a possibility to test many alternative
pre-processing methods in an automated way and optimize the desired classification
or regression performance.
1100
1300
1500
1700
1900
2100
2300
2500
Wavelength [nm]
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Correlation
R
2
2244 nm
Fig. 7.13 Correlation (R) between all NIR variables and the response function (covarygram). The
covarygram shows the correlations between each spectral variable (wavelength) and the response
function, the %DE of Dataset 1
K. M. Sørensen et al.
reflectance at 2244 nm and the degree of esterification %DE is nearly perfect (R
2
=
0.99) albeit in opposite direction (second-derivative points peak downward).
When the pre-processing has been decided and when regression is the target, it is
often useful (but not so often supported by software packages) to plot a covarygram.
This is simply a plot of the correlation of the response value (%DE in Dataset 1) for
each spectral variable.
Figure 7.13 shows such a covarygram made on the MSC transformed spectra. It
immediately visualized that one dominant spectral variable, namely 2244 nm, has a
correlation coefficient of 1.0 to the reference variable %DE. The figure also shows
that large parts of the NIR spectrum contain data that are uncorrelated to the %DE
and therefore can (in principle) be excluded in a multivariate regression model. This
will be further discussed in the variable selection subchapter.
As computers are getting faster and chemometric software packages more and
more complete, most if not all, relevant pre-processing methods will be present in
the software packages. It is sometimes even a possibility to test many alternative
pre-processing methods in an automated way and optimize the desired classification
or regression performance.
1100
1300
1500
1700
1900
2100
2300
2500
Wavelength [nm]
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Correlation
R
2
2244 nm
Fig. 7.13 Correlation (R) between all NIR variables and the response function (covarygram). The
covarygram shows the correlations between each spectral variable (wavelength) and the response
function, the %DE of Dataset 1