## 3 Results and Discussions
### Geographical Prediction Model
Second, a dropout layer was used in the sequential configuration of the artificial neural network, right after the hidden layer of neurons. An immediate improvement in avoiding over-fitting in the structures which presented this unwanted phenomenon was achieved, as shown in Figure 5.  
After constructing several ANN models and observing different alterations of the validation objects' error as new iterations over the training set were performed, it was noticed that 1000 epochs represent a proper choice for the length of the training phase. This is due to the fact that after 1000 iterations, the model does not present any significant improvements. Figure 4: Structure of the ANN developed for the Romania-France classification of honey samples. With the number of epochs fixed, the appropriate combination between the number of neurons, the learning rate value and the probability \(p\) of dropping out neurons had to be found. After testing multiple configurations, the structures which provided the best results were characterized by a number of 30 neurons on the hidden layers, a 0.01 learning rate and a probability of temporary removing hidden units of 20%. With the aim of searching the markers from the elemental and isotopic profiles that play an important role in the geographical classification of the provided honey samples, a first model for predicting the country of provenance (i.e., Romania or France) was developed. Applying the Analysis of Variance (ANOVA) algorithm on the data set in order to obtain the features with the highest classification power, the following results were achieved (i.e., the sorted list of markers, from the most important to the least): Nb, \(\delta^{2}\)H, As, \(\delta^{18}\)O, Ir, V, \(\delta^{13}\)C\({}_{\text{honey}}\), Rb, Fe, Mn, Li, Mo, K, P, Y, Sb, Ba, Mg, Ce, Na, Cu, Pr, La, Cr, Zr, Zn, Ga, Co, Sr, Ni, Al, Pd, Sn, \(\delta^{13}\)C\({}_{\text{protein}}\). Having this insight about the significance of markers in classifying the honey samples based on their country of provenance, new ANN structures were developed in order to observe whether or not the overall accuracies changed when the least important markers (i.e., according to ANOVA) were omitted. Keeping in the analyses vector of all honey objects only the best ten obtained features, the average accuracy increased to 92.27% (\(+/-7.18\)%) from 87.55% (\(+/-8.40\)%). Furthermore, keeping only the most important five markers based on the ANOVA led to an average accuracy of 96.27% (\(+/-6.12\)%) over the 10 folds. Based on these results, it can be stated that reducing the size of the input layer such that it references only the Nb, \(\delta^{2}\)H, As, \(\delta^{18}\)O and Ir markers improves the ANN prediction model by approximately 9%. Moreover, other models were constructed such that one marker at a time was removed from the input layer of the Artificial Neural Network configuration. This method caused some meaningful differences compared to the described model (in which all 34 elemental and isotopic markers were used), suggesting the importance of the elements \(\delta^{2}\)H, As, Fe, Ce, Zr and Co in the regional classification. The significant variations were the ones provided by lower accuracies when removing a certain marker; this means that the prediction model becomes less accurate without a certain element from the analyses vector. For all the other ANN models whose input layer did not include the marker X, where X is different from \(\delta^{2}\)H, As, Fe, Ce, Zr and Co, the average of performances in predicting the country of provenance of the samples decreased. Thus, omitting the analysis values corresponding to X seemed to be a good choice for improving the classification model. However, when developing a new model based on entities having only the six above-mentioned identifiers,  
Figure 5: Avoiding over-fitting by including a dropout layer in the configuration of the Artificial Neural Network: (**a**) Without dropout layer; (**b**) With dropout layer.