## 2 Experimental
### Data Processing. Model Development  
To identify the markers of the elemental and isotopic profiles which provide a higher classification power, an analysis of variance (ANOVA) was applied to the data set in order to obtain the best features from the vector of analyses. ANOVA represents a statistical method utilized for identifying the variations between the means of the provided experimental groups. In this work, one-factor ANOVA was applied, as there exists in the geographical classification only one independent variable (i.e., the honey sample's country of provenance). In a one-factor ANOVA, the computation of the F score (i.e., the Analysis of variance test statistic) involves several measurements for each of the columns in the matrix. In the case of independent classes of entities, a large F value occurs due to a large variance between classes and/or small fluctuations within classes [15]. This counts as the main reason for applying an ANOVA in the process of feature selection; the markers were sorted based on the F value, and the ones having the highest scores were considered to be of greater importance in the classification model.  
Artificial Neural Networks (ANNs) can be classified in feed-forward and recurrent networks. In feed-forward structures there are no cycles, and the computation is made in a uniform way from input nodes to output nodes. Generally, the neurons are organized in layers, and each unit from a specific layer is connected only to units which are part of the next layer. The leftmost layer contains the input units [11] which correspond to the input fields of the training data set of the neural network. In a similar manner, the rightmost layer contains the output units [11] which contain the output of the neural network at a specific time in execution. All the units between these two layers are called hidden units, and they are not directly connected to the outside environment. Neural networks which have in their structure at least one hidden layer are called multilayer networks and are different from perceptrons from this perspective.  
Together with the regional and floral information about the samples, the isotopic and elemental profiles were converted into a Comma Separated Values (CSV) file, from which the developed program transformed each line into a honey sample object having as attributes: a unique id, the country of provenance, the specific region where the honey was produced by the bees and a list of 34 real values consisting of the elemental (e.g., Li, Na, Mg, Al, K) and the isotopic (e.g., \(\delta^{18}\)O, \(\delta^{2}\)H) analyses.  
For developing the prediction models, the Keras Application Programming Interface (API) was utilized at the backend level of the application. Keras serves as an approachable Python-based interface for constructing machine-learning algorithms, established on the top of the end-to-end machine learning platform TensorFlow. As it is thoroughly integrated with the TensorFlow usability, Keras API allows users to customize the provided functionalities, and therefore offers a high degree of flexibility. For common use cases, the Keras API reduces the number of necessary steps; it also displays clear feedback when errors occur. Moreover, TensorFlow 2 and Keras represent the top mentioned options for deep learning in research papers on Google Scholar [16]. The previously mentioned aspects count as the main advantages of choosing and using Keras API in deep learning solutions.