## 4 Conclusions  
The present study proposes a new approach for avoiding the phenomenon of over-fitting in the training set, which is the main drawback in the development of Artificial Neural Networks models when a limited number of samples are available. For this purpose, three main factors had to be taken into consideration: (i) the optimum duration of the learning phase; (ii) the number of hidden units used in the structure of the ANN and (iii) the configuration of the dropout layer. To achieve the optimum duration of the learning phase, no more iterations had to be performed once the error of some testing data started to increase as the error of the training set continued to decrease. The number of hidden units used in the structure of the ANN was obtained by comparing the performance of the ANNs whose configuration differed in terms of this aspect and by selecting the one which presented the best accuracy. The last aspect which proved relevant for preventing over-fitting in the training data was introducing a dropout layer right after the first hidden layer such that some input units are removed by a specified probability \(p\).  
It was noticed that the best obtained accuracy was achieved when reducing the input data to the best five markers (Nb, \(\delta^{2}\)H, As, \(\delta^{18}\)O, Ir) according to the ANOVA algorithm. The neural configuration presented 5 units on the input layer, 30 hidden units and 2 units on the last layer. The chosen activation functions were Rectified Linear Unit and Softmax, and the learning phase consisted in 1000 iterations over the training samples. By using this model, an accuracy of 96.27% was obtained, representing the average of performances over 10 disjunctive folds.  
The following are available online at [[https://www.mdpi.com/article/10](https://www.mdpi.com/article/10)]([https://www.mdpi.com/article/10](https://www.mdpi.com/article/10)) 3390/app11156723/s1, Table S1a: Minimum, maximum and mean values of the measured parameters for the Romanian and French honey samples; Table S1b: Minimum, maximum and mean values of the measured parameters for the Romanian and French honey samples; Table S2: F scores resulted from applying Analysis of Variance, corresponding to each of the measured parameters; Table S3a: Average accuracies obtained by creating ANN structures with different learning rates and distinct number of hidden neurons; probability of dropout: 0.1; Table S3b: Average accuracies obtained by creating ANN structures with different learning rates and distinct number of hidden neurons; probability of dropout: 0.2; Table S3c: Average accuracies obtained by creating ANN structures with different learning rate specifications when constructing the Dropout layer and distinct number of hidden neurons; learning rate: 0.01.  
Conceptualization, D.A.M. and A.R.H.; methodology, R.P., G.C., A.D., F.G. and V.M.; software, A.R.H. and A.J.M.; validation, A.R.H. and A.J.M.; formal analysis, R.P., G.C., A.D., F.G. and V.M.; investigation, D.A.M., R.P., G.C., A.D., F.G. and V.M.; writing--original draft preparation, A.R.H., D.A.M., R.P., G.C., A.D., F.G., A.J.M. and V.M.; writing--review and editing, A.R.H., D.A.M., R.P., G.C., A.D., F.G., A.J.M. and V.M.; project administration, D.A.M.; funding acquisition, D.A.M. All authors have read and agreed to the published version of the manuscript.  
This work was supported by a grant of the Ministry of Research, Innovation and Digitalization, CNCS/CCCDI-UEFISCDI, project number 7 PCE/2021, within PNCDI III.  
Not applicable.  
Data Availability Statement: Data is contained within the article or supplementary material.  
The authors declare no conflict of interest.