El fin de la soberanía nacional

The three previous approaches led to quite similar results, pointing toward the existence of a (hidden) rule that might determine such performance. Nevertheless, no other relationship was found among the variables than a trend to be extracted from spectral areas where the variance of the signal (absorbance) is higher along the different calibration samples, which, in turn, could be the key for a satisfactory classification. The idea has a good chemical background, although, disappointingly, many selected variables concentrated on one of the extremes of the spectrum (Figure 9). These areas mainly are related to spectral noise (noise has a — proportionally — large variance but uncorrelated to the classification problem). To avoid this problem, the GA was forced to skip those variables whose indexes were lower than 25 or higher than 140, and the multimodal search was performed again.

Once the noisiest variables were avoided, a second modification was included to improve the chemical understanding of what was going on. Not in vain, it had been observed many

Concentration Training Validation Commercial

Selected Variables: [88 92] 2%-20% topology ANN=2/10+60/7 lr=0.001 , mseThreshold=2 n=134, #errors=7 n=39, #errors=9 n = 2 , #errors=2 25%-100% topology ANN=2/10+60/5 lr=0.001 , mseThreshold=2 n=86, #errors=3 n=44, #errors=8 n = 21 , #errors=0 Selected Variables: [88 102] 2%-20% topology ANN=2/10+60/7 lr=0.001 , mseThreshold=2 n=134, #errors=4 n=39, #errors=10 n = 2 , #errors=2 25%-100% topology ANN=2/10+60/5 lr=0.001 , mseThreshold=2 n=86, #errors=3 n=44, #errors=7 n = 21 , #errors=0 Selected Variables: [85 102] 2%-20% topology ANN=2/10+60/7 lr=0.001 , mseThreshold=2 n=134, #errors=0 n=39, #errors=11 n = 2 , #errors=2 25%-100% topology ANN=2/10+60/5 lr=0.001 , mseThreshold=2 n=86, #errors=2 n=44, #errors=7 n = 21 , #errors=0

n=number of samples; #=cardinality; lr=learning rate; mseThreshold: mse threshold used to stop training (if it does not stop after 500.000 cycles)

times that the selected variables did not have a chemical meaning, so we could not determine which carbohydrates defined precisely the quantity of apple juice at the beverages. In order to solve this major chemical issue, the GA was fed information regarding the spectral areas that can be associated specifically to the most important carbohydrates (Figure 9). In such a way, the GA will favour those individuals whose variables are closer to those of the carbohydrates.

Table 7 resumes the results of several studies. It can be observed that the classification success is similar — or even slightly superior — to those obtained with multimodal search alone. But, now, the main carbohydrate/s (sugar/s) responsible for the classification model is/are known.

Conclusions

Several conclusions can be derived from the results obtained with the use of different proposals for variable selection:

• The EC techniques, particularly GA, demonstrated that they are a valid way to perform variable selection, since their results were, in general, acceptable. • The classification success for the pruned search approach is greater than for the

fixed search one. This can be explained because the likelihood of joining variables that, together, can offer a good result is lower when the chromosome has only two genes, than when, on the contrary, a sequential — pruned — search is applied. In the latter case, a progressive elimination of variables is undergone until (in the case study presented here) the two most important variables remain.

• Best results were obtained using a multimodal GA, likely because of its ability to maintain the diversity of the genetic population. Such diversity not only induces the appearance of optimal solutions, but also avoids the search to stop on a local minimum. This option not only provides a solution, but a group of them with similar fitness. This allows chemists to select a solution with a sound chemical back- ground. A particular, highly appealing approach is to include “points of interest” into the GA searching strategy, namely the HTP-GA.

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Section IV