The combination
of a principal component analysis with neural networks is a fast and efficient
way of compressing the information fed to the neural networks. Yet, the decision
how many principal components to use for the neural networks remains a problem
as this determines the extent of compression and the extent of information loss
similar to the PLS (see section 2.5). Thus, neural networks
with 6 hidden neurons in 1 hidden layer were trained with a systematically increasing
number of principal components from 1 to 40 and the crossvalidation error of
the calibration data was determined. The optimal models in terms of lowest crossvalidation
errors were obtained by networks using 25 principal components for R22 and 16
principal components for R134a. According to table
2, the prediction errors of the external validation data (2.16% for R22
and 3.24% for R134a) are practical identical with the fully connected neural
networks. In addition, the true-predicted plots and the statistical tests are
practically identical and will not be discussed any further here. The negligible
gap between the calibration errors (1.98% for R22 and 3.08%) and the validation
errors indicates that the reduction of the number of parameters (157 for R22
and 103 for R134a) successfully prevents an overfitting of the calibration data.
Yet, the predictions of the validation data and with it the generalization ability
are not significantly improved, which might be ascribed to some general drawbacks
of the variable compression by the PCA already discussed in section
2.8.7.