## 4 Results and Discussion
### AI-Based Models Employed for the Feature Engineering Task  
Figure 11 displays the optimal set of predictors for PM\({}_{2.5}\) and PM\({}_{10}\) concentrations as identified by each feature selection (FS) technique evaluated. Figures 12 and 13 present the statistical analysis results for the best feature combinations selected by the 50 FS techniques tested. Among these, the GEO model demonstrated the highest prediction accuracy for both PM\({}_{2.5}\) and PM\({}_{10}\) concentrations. For PM\({}_{2.5}\), the GEO model identified the following variables as the most relevant predictors: Benzene, CO, m-Xylene, NO\({}_{2}\), NO\({}_{\omega}\), o-Xylene, Ozone, Precipitation, Relative Humidity, SO\({}_{2}\), Temperature, Wind Direction, and Wind Velocity. The statistical performance of this model is summarized as follows:  
* Training phase: R\({}^{2}\) = 0.88, MBE = 0 \(\mu\)g/m\({}^{3}\), RMSE = 10.27 \(\mu\)g/m\({}^{3}\), MAPE = 0.70, \(\sigma\) = 10.28 \(\mu\)g/m\({}^{3}\)
* Testing phase: R\({}^{2}\) = 0.86, MBE = 0.69 \(\mu\)g/m\({}^{3}\), RMSE = 9.25 \(\mu\)g/m\({}^{3}\), MAPE = 1.49, \(\sigma\) = 9.24 \(\mu\)g/m\({}^{3}\)  
For PM\({}_{10}\), the best feature set included all variables except relative humidity. The corresponding performance metrics are:  
* Training phase: R\({}^{2}\) = 0.80, MBE = \(-\)4.17 \(\mu\)g/m\({}^{3}\), RMSE = 21.26 \(\mu\)g/m\({}^{3}\), MAPE = 1.40, \(\sigma\) = 20.86 \(\mu\)g/m\({}^{3}\)
* Testing phase: R\({}^{2}\) = 0.67, MBE = \(-\)2.94 \(\mu\)g/m\({}^{3}\), RMSE = 23.63 \(\mu\)g/m\({}^{3}\), MAPE = 3.78, \(\sigma\) = 23.48 \(\mu\)g/m\({}^{3}\)  
In contrast, other FS techniques demonstrated significantly lower correlation and weaker predictive accuracy for PM\({}_{2.5}\) and PM\({}_{10}\) concentrations, further highlighting the superior performance of the GEO-based approach in identifying meaningful predictor sets. Figure 11: The best combinations of inputs found by each FS method in predicting hourly PM\({}_{2.5}\) and PM\({}_{10}\) concentrations. A comparative performance is provided by Table 7, which shows the evaluation metrics for the best model trained using all features versus that trained on the optimal subsets for PM\({}_{2\text{-}5}\) and PM\({}_{10}\). The results confirm that using the selected optimal features improves or maintains predictive accuracy while reducing model complexity. This comparison strengthens the case for using feature selection and aligns with the original objective stated earlier in the manuscript. PM\({}_{2.5}\) models show consistently better performance compared to PM\({}_{10}\) models. The first reason is that PM\({}_{2.5}\) exhibits stronger correlations with other studied variables compared to PM\({}_{10}\). This suggests that PM\({}_{2.5}\) is more closely linked to the selected predictors, which likely contributes to the higher predictive accuracy observed in the PM\({}_{2.5}\) models. In general, models built using strongly correlated input variables tend to achieve better performance, as is evident in the case of PM\({}_{2.5}\). The second reason is connected to data quality and sensor sensitivity: PM\({}_{2.5}\) data, collected from the monitoring stations, is more consistent and less prone to measurement errors or local anomalies than PM\({}_{10}\). The lower \begin{table}
\begin{tabular}{c c c c c c c} \hline Target & Model & R & MBE & RMSE & MAPE & Sd & Rank \\ \hline \multirow{3}{*}{PM\({}_{2.5}\)} & xGBoost & 0.92 & 0.19 & 9.60 & 1.32 & 9.61 & 1 \\ \cline{2-7}  & xGBoost-GEO & 0.91 & 0.64 & 8.07 & 1.27 & 8.05 & 1 \\ \hline \multirow{3}{*}{PM\({}_{10}\)} & RF & 0.83 & 1.05 & 19.45 & 3.03 & 19.45 & 1 \\ \cline{2-7}  & RF-GEO & 0.77 & \(-\)0.65 & 21.91 & 3.39 & 21.92 & 1 \\ \hline \end{tabular}
\end{table} 
Table 7: A comparative performance between the best model trained using all features versus that trained on the optimal subsets (for testing stage). Figure 12: A comparison of FS techniques in predicting PM\({}_{2.5}\) concentration in the training and testing stages.