## 3 Results and Discussion  
For the development of the geographical recognition models, the isotope and elemental profiles of 117 Romanian and 19 foreign (i.e., having as their geographical origin countries other than Romania) samples were determined. In order to build the most suitable model for this purpose, three machine learning (ML) algorithms, namely artificial neural networks (ANN), support vector machines (SVM) and k-nearest neighbors (KNN), were applied, and then their efficiency was assessed and compared. Three types of input spaces were used for the development of the prediction models. The first one included all 54 experimental attributes (i.e., the entire set of isotope and elemental determinations), while the other two implied a dimensionality reduction step. In this regard, a model-based feature selection based on a supervised method (i.e., PLS) and an unsupervised method for transforming the original data into a smaller set of attributes that capture as much of the data set's variance (i.e., PCA) were applied. The first category of models for the geographical differentiation of the honey samples aimed to discriminate the Transylvanian samples from the ones that had as their geographical origin other regions in Romania. When all the isotope and elemental measurements were used as input data, the ML algorithm that conducted to the best classification results was represented by SVM (Table 1). Through this approach, a model having 75% accuracy was obtained; namely, 98% of the Transylvanian samples and 36% of the ones originating from other Romanian regions were correctly attributed to their corresponding group. The other two ML models (i.e., ANN and KNN) led to similar accuracy scores (73%), succeeding in predicting the geographical origin for 71 out of 96 samples. Even though the performance of these two methods in terms of accuracy was the same, an interesting aspect is reflected by the fact that ANN proved to have the highest ability in predicting the geographical class of the samples originated from regions other than Transylvania. When the input data for the construction of the prediction models was reduced to the scores on the first 10 principal directions found through PCA (i.e., that explained more than 70% of the data set's variance), the only type of classifier that outperformed the ones constructed on all attributes was the ANN model. In this case, an overall accuracy of 76% was achieved, though the dimensionality of the input space was more than five times smaller than the initial one. Selecting a subset of relevant markers through a supervised method has proven to be the most efficient approach for reducing the dimensionality of the input space. It was previously reported that by the employment of a supervised data reduction step before the recognition model development, an important improvement of the prediction rate can be achieved [32; 33]. This is due to the fact that not only did this technique conduct to more accurate results than the ones achieved when the input data corresponded to the scores of the initial points on the first 10 principal components, but it also outperformed the initial ML classifiers (Table 1). The model-based attribute selection allowed the decrease of the input space to the following 19 features: \(\delta^{2}\)H, B, V, Mn, As, Sr, Nb, Pd, In, La, Ce, Pr, Nd, Tm, Pt, Tl, Pb, Mg and Ca (Table S1). Based on this input data, the most accurate ML models corresponded to ANN and SVM, which managed to correctly classify 85% and 84% of the samples, respectively. The robustness of the models was also reflected by the fact that both of them were able to identify the correct geographical source of 72% of samples