## 4 Data Sets and Experimental Results
By reducing the dimensionality of the input data, this approach not only streamlines the model training process but also minimizes the risk of introducing sparsity, which can lead to degraded model performance. The evaluation of neural network models was performed using a 10-fold, stratified cross-validation. The following measures of classification quality evaluation were used: the classification accuracy measure (_acc_)--that is, a fraction of the total number of objects in the test set that are classified correctly; recall, which expresses the classifier's ability to correctly recognize the given class; precision (Prec. ), which expresses how often the classifier does not make a mistake when classifying an object to a given class; and the F-measure (F-m.), which is an aggregate measure that assesses whether the classifier is capable of keeping accuracies balanced. \[\text{F-measure }=2\cdot\frac{\text{Precision}\cdot\text{Recall}}{\text{ Precision}+\text{ Recall}} \tag{13}\]  
MLP and RBF networks were used during the experiments. For the MLP network, the following parameters were checked:  
* One and two hidden layers with different numbers of neurons per layer. The following combinations were tested:
* One hidden layer with 30, 50, 70, and 100 neurons;
* Two hidden layers with (30, 10), (50, 30), (70, 50), and (100, 80) neurons in the first and second layers, respectively. * The following activation functions for the hidden layer were used:
* The rectified linear unit function, \[f(x)=\max(0,x),\] (14)
* The hyperbolic tan function, \[f(x)=tanh(x),\] (15)
* The logistic sigmoid function, \[f(x)=\frac{1}{1+\exp(-x)}.\] (16)
* The following optimizer was used:
* Stochastic gradient descent [31];
* The Adam optimizer proposed in [32]. * Both optimizers were used with an initial learning rate that controlled the step-size in updating the weights equal to 0.001, 0.005, 0.009, and 0.01;
* The following numbers of epochs were used: 500, 700, and 1000;
* The neural network was trained using the back-propagation and stochastic gradient descent methods. For the RBF network, the following parameters were checked:  
* This network always includes one hidden layer, but the number of neurons are parameterized by the number of neurons in the input layer. The following values were analyzed: \(\{0.5,1,1.5,2,2.5,3,3.5,4,4.5\}\times\) the number of neurons in the input layer, which was equally the number of attributes after pre-processing. Exactly the following values were checked: 64, 127, 190, 254, 318, 381, 444, 508, and 572 neurons. * The number of training samples used in one iteration(batch size) was equal to 200. * The number of epochs--one full cycle through the training data set--was equal to 450. Additional experiments were carried out using the recurrent neural network model (RNN). Due to time constraints, only the gated recurrent unit (GRU) model was used with the following parameters. The model has one hidden layer with a parameterized number of neurons. The values analyzed are as follows: \(\{3,3.5\}\times\) the number of neurons in the input layer. The code that was used defines a neural network using the Keras library in Python. A comparison of experimental results was performed in terms of the following:
* The quality of classification for the MLP network and the RBF network;
* The quality of classification for neural networks and approaches from papers [24; 25] that use fuzzy-based decision rules and rough-set decision rules. The selection of hyper-parameters for the models experimented with in this paper (i.e., the activation function, learning rate, and optimizer) was based purely on empirical evidence. In an iterative way, different parameter values for the learning rate, activation function, and optimizer, as well as the neuron number in subsequent layers, were experimented with, and the parameter-value combination that provided the optimal results was used.