# Clustered Distributed Learning Exploiting Node Centrality and Residual Energy (CINE) in WSNs
## 4 Performance Evaluation
### Numerical Results  
In this section, we report the numerical results obtained in the scenario described in the previous section by applying the CINE protocol. We conducted large simulation campaigns to estimate the average loss with respect to the number of iterations for different types of centrality, \(\alpha\), and threshold, \(\sigma_{TH}\), values. We also evaluated the average residual energy  
Figure 3: Wireless network scenario considered for the simulations. at each cluster. Note that the residual energy was evaluated in terms of percentage for generalizing the exploitation of any kind of short-range (low TX power)/long-range radios (high TX power) in a WSN scenario. We assumed that the node exploits the bluetooth low energy for the short-range radio (the low-power TX mode case) and LoRa for the long-range radio (the high-power TX mode case). Since bluetooth low energy has a power consumption of 50 mW and LoRa has a power consumption of 150 mW [44, 45], we considered the energy consumption in the long-range radio to be 10 times that of the power consumption in the short-range radio as both bluetooth low energy and LoRa can communicate at the same data rate in specific settings. Finally, we calculated the average number of data chunk transmissions with respect to different threshold \(\sigma_{TH}\) values. Note that the loss metric considered in this paper is the _medium square error_ (MSE), which is calculated as  
\[MSE(y,\hat{y})=\frac{1}{\mathcal{N}}\sum_{i=0}^{N}(y-\hat{y}_{i})^{2} \tag{4}\]  
where \(y\) is the input data fed into the autoencoder, \(\hat{y}\) is the reconstructed output data, and \(\mathcal{N}\) is the length of the input data. In Figure 4, we report the average loss with respect to the number of iterations for different centrality metrics. We observe that the eigen, pagerank, and degree centrality metrics give similar results, while the average loss in the case of betweenness centrality is significantly higher. Accordingly, in this section we will present the results achieved by applying the degree centrality. In fact, eigen and pagerank centrality give similar results, whereas betweenness centrality gives much worse results and thus must be excluded. In Figure 5, we report the average loss with respect to the number of iterations for different values of \(\alpha\). Note that \(\alpha\) is the parameter that weights the importance given by each CH to the models received by another CH, as given in Equation (1). From Figure 5, we observe that the convergence is faster when the \(\alpha\) is higher. \(\alpha\) corresponds to the tuning parameter in the weight update Equation (1). If the value of \(\alpha\) is higher, it means more priority is given to the model parameters that were just received than the nodes current model parameters. If the \(\alpha\) value is lower, it means that less priority is given to the model parameters that were just received than the nodes current model parameters. From Figure 5, it is observed that the convergence is faster when higher weightage is given to the model parameters that were received by the nodes. Figure 4: Average loss vs. number of iterations for different centrality metrics. In Figure 6, we report the average loss with respect to the number of iterations for different values of the threshold \(\sigma_{TH}\). In the first 20 iterations, the average loss decreases quickly when the threshold is low. The reason for this occurrence is that the data chunk transmissions are more frequent when the threshold is low; therefore, the models are trained considering more data. More specifically, a lower threshold will result in the high frequency of transmission of data chunks from the cluster members to the cluster heads. This will enable the cluster head to train with more data. Hence, the performance of the model is enhanced, resulting in lower average loss. In Table 1, we report the average residual energy at each cluster after 80 iterations. Clusters 1 and 2 have higher residual energy after 80 iterations than Clusters 3, 4, and 5.