## 3 Results and Discussion
### Artificial Neural Network  
Another powerful form for ML model's implementation is the ANN. An ANN resembles the function principles of a human's brain. The analogy is that, in place of the brain neurons, an ANN model uses the nodes that deliver the signal's information within the network. The basis of an ANN is the perceptron, which receives an input signal \(x_{i}\) with a weight of \(w_{i}\) and a bias \(b\), added through a summation junction and then passed through an activation function \(f\) to provide the final output, as shown in Figure 11. All these complex combinations of input signals, weights, activation functions and biases for each layer allow for a sufficient modeling of highly non-linear relationships. The perceptron transfer function can then be expressed as [42],  
\[y=f(\sum_{i=1}^{n}W_{ji}x_{i}+b) \tag{7}\]  
The internal layer perceptrons, those in between the input and output layers, receive the summed weighed values of the input parameters (i.e., temperature, pressure, dew point, solar flux, wind speed, relative humidity and air-sea temperature difference) and provide the \"input\" signal for the output layer. All three layers are fully connected to each other. The proposed ANN architecture contains seven nodes in the input layer and a single node in the output layer RSSI, which receives the weighted input signals from the hidden layers along with a bias and represents the values of the predicted variable. The  
Figure 11: The multilayer perceptron network architecture for RSSI prediction. Figure 10: Feature importance (**left**) and permutation importance (**right**) for the GBR model estimators. architecture of our model is a multi-layer perceptron model (i.e., shallow neural network) and the input-output mapping can be represented as follows:  
\[y=g(\sum_{j=1}^{m_{1}}W_{j}f(\sum_{i=1}^{n}W_{ji}x_{i}+b)+c) \tag{8}\]  
where \(g\) is the transfer function and \(c\) is the bias for the output layer. Other ANN architectures could include more than a single hidden layer. The transfer function to characterize the hidden layer, can be one of the following functions, [42]:  
\[\text{Tangent Hyperbolic Function}:\ f(x)=\frac{(e^{x}-e^{-x})}{(e^{x}+e^{-x})} \tag{9}\]  
\[\text{Sigmoid Function}:\ f(x)=\frac{1}{1+e^{-x}} \tag{10}\]  
\[\text{Rectified Linear Unit }(\text{ReLU})\ \text{Function}:\ f(x)=\max(0,x) \tag{11}\]  
\[\text{Gaussian Function}:\ f(x)=e^{-x^{2}} \tag{12}\]  
\[\text{Linear Function}:\ f(x)=x \tag{13}\]  
We used a standard Levenberg-Marquardt learning method to train a two-layer feed-forward network with sigmoid hidden neurons and linear output neurons for an extended number of nodes (i.e., 2-100) in order to map the macroscopic meteorological parameters obtained from the weather station to the RSSI parameter obtained from the PSO system. The neural net fitting application of MATLAB was used to perform all the ANN computations. The ANN algorithm applies a three-fold division of the entire data set (i.e., the training, validation and testing subsets). The training data subset is presented to the network during training and the network is adjusted according to its error. The validation subset is used to measure the generalization of the network and stop the training when generalization stops improving. The testing subset is used to independently measure the performance of the network after training. Seventy percent of the entire data set was assigned to the training of the network, fifteen percent to the training validation, and fifteen percent for the network's performance testing. Figure 12 shows the performance of the MLP ANN algorithm for the RSSI prediction based on the seven meteorological parameters. We trained, validated and tested the algorithm for different numbers of nodes of the hidden layer, which resulted in significant decrease of the model prediction error approximately up to the 20 th node. A further increase in hidden layer nodes provides slightly better results but also a substantially bigger computational cost.