## 4 Data Sets and Experimental Results
Also, the motivation for choosing the Gaussian kernel for the RBF neural networks was justified by its localized activation [33], smoothness [34], computational simplicity [35], and well-established property as a universal approximator [36].The Gaussian kernel's ability to balance complexity and generalization makes it an optimal choice as the kernel for the RBF network. It is important to note that neural networks are prone to over-fitting due to their complex structure, which usually captures very intricate patterns during training. For instance, since RBF networks rely heavily on localized responses, mainly due to the model's sensitivity to input distances, it becomes susceptible to over-fitting. To overcome the issue of over-fitting, for all the models used in this paper (MLP, RBF, and RNN), batch normalization and dropout-layer techniques were employed. By normalizing the input to each subsequent layer (from the input layer), the possibility of the data distribution varying greatly was avoided, making the model learning more effective and the convergence rate faster. After batch normalization, a.25 dropout rate was applied to ensure the prevention of over-fitting by forcing the network to generalize well across multiple neurons. In all, while batch normalization facilitates smoother training, dropout introduces robustness and prevents the model from learning patterns that do not generalize well. Tables 2 and 3 present the average classification accuracy measure (_acc_), recall, precision (Prec. ), and F-measure (F-m.) obtained using the 10-fold cross validation method. In Table 2, for the MLP network, only the best result from all tested parameters values is shown in the table. This is the result obtained for the following values: one hidden layer with 50 neurons, the logistic activation function, the Adam optimizer, and an initial learning rate equal to 0.005. For RBF networks, the results are given for different numbers of neurons. The best result is in bold. Table 3 shows the results for the GRU model. As can be seen in Table 2 the MLP model makes fewer false positive predictions, and the overall correctness of the model across all classes is higher than that of the RBF model. The accuracy for the MLP model is almost perfect and is at a very high level of 0.999. So, it can be implemented successfully in practice to predict which customers will stay with the company. On the other hand, the ability of the RBF model to correctly identify all positive instances is better. That also leads to the consequence in which the F-measure, which provides a single score that balances both precision and recall, is higher for the RBF model. So, in practice, this model can be used to predict which customers to pay more attention to and offer promotions to keep them using a mobile service. The GRU model (Table 3) performs much worse than the MLP and RBF models in terms of each measure. To measure how the models perform against imbalanced data sets (as is the case for the churn data used in this paper), ROC curves were generated for each model. As can be seen in Figures 3-6, the MLP model and the RBF models exhibit a very high value, indicating that these models can effectively distinguish between the positive and negative classes of the churn data set. In the case of the GRU model (Figure 7), however, the model is not as effective in predicting both positive and negative classes of the data set. As is known, neural networks are black boxes, and unfortunately, they do not provide clear and readable rules based on which a human could easily understand a model's prediction. As can be seen, the predictive ability of the neural network model is high, but the interpretability of the model is entirely lacking. Comparing with the resultsobtained in papers [24; 25], where fully interpretable models were used, which generated clear and readable decision rules, reveals that both aspects should be taken into account.