## 3 Results  
### Model Performances  
Fine tuning the LOF model to achieve the best possible silhouette score was performed by running different combinations of the n_neighbours and contamination parameters. The n_neighbours parameter specifies the number of neighbours considered when calculating the LOF score, while the contamination parameter defines the expected proportion of outliers in the dataset. The results of the applied grid search can be seen in Table 3.  
Despite the best silhouette score being observed at a 0.005 contamination rate and 15 n_neighbours, the model with a contamination rate of 0.01 was chosen, with its results shown in Figure 4b. This was decided due to the small number of data points existing in the dataset, with 0.005 limiting the number of anomalies to only eight data points. The more anomalies that are detected, the less likely it is for the model to misclassify an actual leak as normal.  
The machine learning-model-predicted leak locations are shown in Figure 4a for the GWR model and in Figure 4b for the LOF model. Note that since leakage causes drops in the values of the three independent variables, positive standard deviations of the dependent variables were used to determine the possible leak locations. GWRs of pressure, flow, and chlorine show large numbers of sites with positive and negative residual values, indicating a lack of stationarity across Sharjah (Figure 4a). Moreover, these variables show similar sub-regions with high positive residuals in industrial areas of the region, leak locations A, B, C, and D, suggesting some parallel localized dependency on the high density of residuals. A geographic pattern was observed where residuals are stationary throughout most of the study area, with some clusters of high residual variation in the western part (Figure 4a), and an isolated patch of low residual variation in the western part of the study areas because there are fewer settlements. The obtained coefficient of determination (R\({}^{2}\)) for the GWR model was 0.909. The main advantage of using GWR in this study is to explore the varying spatial relationships between the three parameters (the explanatory variable) and the leakage as the dependent variable. The results show that the relationship between the leakage (dependent variable) and the explanatory variables is spatially consistent. The high  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**n\_Neighbours**} \\ \hline
**Contamination** & **2** & **5** & **10** & **15** \\ \hline
0.005 & 0.0247 & 0.0688 & 0.2525 & 0.3478 \\ \hline
0.010 & 0.0080 & 0.1050 & 0.2144 & 0.3404 \\ \hline
0.050 & \(-\)0.0476 & 0.0038 & 0.1480 & 0.1378 \\ \hline
0.100 & \(-\)0.0298 & 0.0091 & 0 degree of correlation indicates the suitability of the model. Figure 5 shows a comparison between the results of the GWR and LOF models, which showed an overall match of 80% in the dataset. Note that in the figure, a circle shows a match and a rectangle shows no match between the models, only for the visually clear leak locations. A match of 80% is also indicative of the effectiveness of this particular model.  
Figure 4: The predicated leak locations using the GWR and LOF models.