Biomedical Engineering Reference
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be superior to alternatives such as manual wavelength selection or principal
components analysis because the PLS decomposition automatically finds a
linear combination of the variables that is optimal for LDA [26].
The number of latent variables was chosen by a cross-validation [24] in
which all the spectra from one sample of each type were left out of each itera-
tion. The obtained misclassification rate was 0% with two latent variables.
After cross-validation, the PLS-DA model was calculated from the full
training set and applied to both the training and test sets; the results are
shown in FigureĀ 6.3.
The high-dimensional spectral space has been reduced to a two-dimensional
space of PLS scores (T1 and T2). All the spectra are correctly classified, and the
test samples fit closely with the training samples.
10
5
S-1, 3, 5
0
-5
R-1, 3, 5
-10
-5
0
5
10
T1
(a) Calibration set
10
5
0
S-2, 4, 6
-5
R-2, 4, 6
-10
-5
0
5
10
T1
(b) Te st set
Figure 6.3
PLS-DA scores for (a) the calibration set and (b) the test set.
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