## 5 Discussion
### Comparing Scenarios  
This section compares the prior results from the MIS theoretical application with the performance of MP facilities currently operating in Recife, taking into consideration the case for a 3 km radius coverage, aims to investigate differences in the performance of both scenarios, and suggests concluding remarks based on the proposed model to aid policy decisions regarding public safety. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Coverage** & **Number of Police** & **Optimal** \\
**Radius (Km)** & **Occurrences Covered** & **Coverage Rate** \\ \hline
1.00 & 582 & 34.5\% \\
1.50 & 923 & 54.7\% \\
2.00 & 1143 & 67.7\% \\
2.50 & 1380 & 81.8\% \\
3.00 & 1521 & 90.1\% \\
3.50 & 1630 & 96.6\% \\
4.00 & 1664 & 98.6\% \\
4.50 & 1675 & 99.2\% \\
5.00 & 1683 & 99.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal coverage. Figure 8: Optimal police facility allocation for 3.0 km coverage. Figure 9 provides the main results of this comparison. The illustration exhibits the performance of the proposed MIS in relation to the current configuration of police facilities in Recife (MP). The gain in the coverage of occurrences per facility is evident in Figure 9. The new police facility locations provide additional coverage in relation to the current configuration. Using the proposed MIS reports, it is possible to reach, at the end of the fifth allocated installation, a 90% coverage of occurrences, representing a 22% improvement compared to the current scenario. The 22% improvement is more perceptible when analyzing this scenario with the number of police occurrences covered. Between 2012 and 2017, a total number of 1688 police occurrences were recorded using the platform 'Onde Fuji Roubado'. Considering the case of a 3 km radius coverage, of the total of 1688, only 167 crimes would not be covered if the police centers were established in the places suggested by the MIS, compared to 532 crimes that would not be covered by the current police center locations. This difference is significant given the magnitude of the evaluation. Due to problems with sub-notification and unreported occurrences, these rates could be higher. Continuing the comparative analyses, from a spatial perspective, Figure 10 illustrates a significant reduction in the operating distance for a police patrol from the optimized locations to the occurrences. Figure 10 illustrates this additional prospect. It can be observed that the proposed model manages to significantly reduce the average distance of occurrences in relation to the current configuration of the MP. Achieving a significant difference, which can be extended to 920 m considering the fifth allocated facility, positively reduces the time that a police vehicle needs to leave the facilities and arrive at the locations of crimes. Table 3 reports a sensitivity analysis of the different numbers of candidates for five allocated facilities and a coverage distance of 3 km. Table 3 reports a slightly better coverage percentage for K > 20 candidates compared to the 10 adopted candidates, as expected. As k-means attempts to divide data equally along the space, keeping everything else constant, increasing the number of candidates can also provide great coverage after optimizing Euclidean distances for the allocation of facilities. In the extreme case when the number of candidate points is equal or close to the number of criminal occurrences (the last rows of Table 3), the methodology indicates a single cluster for each feature, which makes it useless. For K = 5 candidates, there is also a slightly better coverage percentage. The authors in [70] describe this as a regularization problem, and it has the same explanation as that described above. Occurrences are closer and closer to a cluster centroid as K increases. This can create a distor  
Figure 9: Performance comparison (coverage).