## 3 Results and Discussions  
### Model Construction. Limitations and Optimizations  
The number of hidden layers, the number of neurons on each hidden layer and the number of iterations in the learning phase of the network were initially chosen following the idea according to which, after multiple runs, the preferred configuration was the one which resulted in the smallest error which did not present any significant decrease at the end of the learning phase. This approach led to over-fitting the training set, mainly because of the honey set size, which did not comprise a large number of samples. Over-fitting limitation  
Over-fitting defines the situation in which the algorithm corresponding to the learning phase of an ANN provides very good results for the training set, but untrusty predictions for testing data. This phenomenon is more likely to appear when dealing with a limited amount of data; the size of the data set is considered to play an important role in avoiding the acquisition of information about the noise and the particularities of the training collection (i.e., over-fitting). This implies that at a certain point, during the learning phase, the in-development Artificial Neural Network does not improve in predicting the testing data, even though it continues to offer more accurate results for the training set (i.e., the error for the testing entities increases as the error for the training entities decreases); the phenomenon is illustrated in Figure 2.  
One approach for avoiding this unwanted situation is applying early stopping, meaning that no more iterations over the training set should be performed once the error begins to increase on the validation entities [17]. Furthermore, it has been observed that the number of neurons present in the hidden layers has a high impact on whether or not the trained ANN is predisposed to encounter over-fitting of the training set; a surplus of neurons in the hidden structure of the network lead to over-fitting. This is due to the fact that the hidden neurons affect the error of other neurons to which they are linked and consequently the overall error of the ANN. Another successful method for preventing over-fitting is applying dropout, a technique through which neurons are temporarily removed from the artificial neural structure. This implies the fact that the units are dropped out together with their input and output connections to other neurons, with a probability \(p\)[18]. Applying dropout to the hidden units during the training phase of the ANN proved to reduce the generalization of the training set and led to better accuracy results. In this work, a new approach for the obtainment of a good model accuracy for honey geographical origin prediction (Romania vs. France) was envisaged. For this purpose, different attempts were performed to find the most adequate model, and at the same time to avoid the over-fitting effects, by comparing the performance on the testing set when changing the number of iterations, the number of hidden neurons and the probability \(p\) of dropping out neurons. Figure 2: Over-fitting phenomenon: the loss corresponding to the validation data (val.) starts to increase around the epoch 400, whereas the loss of the training data (train) continues to decrease in value. In order to design a reliable discrimination model, two procedures were applied for dividing the data set into training, validation and testing samples. The first approach was k-fold cross validation (Figure 3), a method in which the entire data set is randomly separated into k non-overlapping sets containing approximately the same number of entities. Each group is taken consecutively as input data for testing the developed predictive model constructed on the information provided by the other k - 1 folds. Thus, the overall accuracy of the ANN structure can be seen as an average of the performances achieved by testing each of the k folds.