## 4 Summary and Conclusions
\begin{table}
\begin{tabular}{c c c c} \hline \hline
\begin{tabular}{c} **Standard of** \\ **Categorization** \\ \end{tabular} & \multicolumn{2}{c}{**MRA**} & \multicolumn{1}{c}{**DNN**} \\ \cline{2-4}  & **Leakage Management Model Formulation** & & **R** \\ \hline GeJ & \(Y_{Gd}=-0.34X_{2}-4.59X_{3}+19.28X_{4}+1.68\) & 0.75 & 0.76 \\ \hline GR & \(Y_{GR}=0.35X_{1}+0.24X_{2}+11.05X_{3}+14.07X_{4}-18.62\) & 0.98 & 0.82 \\ \hline GS & \(Y_{GS}=0.35X_{1}+0.30X_{2}-2.22X_{3}-20.35X_{4}-6.37\) & 0.91 & 0.92 \\ \hline NJ & \(Y_{NJ}=0.12X_{1}-0.11X_{2}-7.57X_{3}+16.26X_{4}+1.53\) & 0.77 & 0.84 \\ \hline DDC & \(Y_{DDC}=-0.06X_{1}-0.10X_{2}-72.42X_{3}-13.54X_{4}+5.50\) & 0.85 & 0.86 \\ \hline BH & \(Y_{BH}=-0.14X_{1}+0.03X_{2}-10.64X_{3}+13.99X_{4}-15.41\) & 0.99 & 0.99 \\ \hline SC & \(Y_{SC}=-0.40X_{1}-0.18X_{2}+30.92X_{3}-21.09X_{4}-2.51\) & 0.76 & 0.85 \\ \hline SS & \(Y_{SS}=0.22X_{1}+0.03X_{2}-3.59X_{3}+26.57X_{4}-1.13\) & 0.9 & 0.86 \\ \hline JE & \(Y_{JE}=-0.19X_{1}+0.01X_{2}+22.64X_{3}+14.56X_{4}-6.19\) & 0.99 & 0.99 \\ \hline TY & \(Y_{TY}=0.22X_{1}-0.38X_{2}+1.47X_{3}-1.90X_{4}+5.06\) & 0.82 & 0.87 \\ \hline HP & \(Y_{HP}=0.50X_{1}-0.09X_{2}+1.67X_{3}+35.71X_{4}-6.39\) & 0.87 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of deriving leakage management model formulation considering spatial and temporal characteristics. water loss management activity. Lastly, regarding the various analyses in this study, in most of the classification groups, depending on the revenue water ration and the leakage ration, the DNN model of the coefficient of determination was higher than MRA. Moreover, in the second analysis, the performance of data analysis using DNN is more appropriate in the data classification considering the characteristics of time series compared with independent data analysis. Therefore, it can be judged that DNN is a suitable model for the formulation of water loss management. Through the comparison of the above data classification approaches, the increase or decrease in the leakage ratio/revenue water ratio by the water loss management activity of local WDSs can be used to construct a more effective model for classification, considering both local and temporal characteristics. The results of this study are expected to be highly useful when analyzing leakage management efficiency and determining the leakage management goals of WDSs with similar size and characteristics in the future. In particular, it can be used as a basis for determining project goals and budgets at the planning stage, and it can also be used for prioritization and evaluation of each leakage reduction activity to achieve project goals. In addition, it will be possible to derive a water leakage reduction plan with optimal efficiency by evaluating the current pipeline conditions according to the leakage ratio/revenue water ratio, selecting the pipeline maintenance target, and reducing the water leakage through pressure control. Finally, it will be possible to prioritize pipeline maintenance in order to increase leakage reduction efficiency by calculating the amount of leakage reduction for each pipeline. Conceptualization, Y.H.C. and T.C. ; data curation, T.C. ; methodology, D.G.Y. and Y.H.C. ; supervision, S.L. ; writing--original draft, Y.H.C. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Research Foundation of Korea (NRF) (NRF-2021R1G1A1003295). Not applicable. The data are not publicly available. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government. There is no conflict of interest, and the source of funding, including the grant number for this paper, have been declared.