## 3 Experiments and Results
### Geographical and Spatiotemporal Analysis  
As previously explained, two available variables in our DB were latitude and longitude of the emergency events. With this information, it was possible to geolocate these on a map for visual and numerical analysis of the geographical characterization of the FRIs under study. Although these types of geographical phenomena analyses and visualizations are being deeply studied [22; 23], heatmap visualizations based on KDE approaches are one of the most widely applied solutions [24; 25]. This popularity is due to their easy-to-modify character, in order to create efficient and scalable  
Figure 7: Temporal representation of the confidence interval (CI) of events during 2014, for police (**a**); health (**b**); and transit (**c**) services; as well as fire brigade events over 4 years, from 2013 to 2016 (**d**). Dashed lines are the criterion used to identify the OE, and gray areas are used to characterize the repeating patterns and subsequent resource allocation by managers. versions for different types of data, such as data streams [26; 27] or big data [28; 29; 30]. For this reason, heatmap visualizations based on improved KDE methods have been used in a wide range of application fields, including traffic data visualization [31], emotional heatmaps [32], sentiment analysis [33; 34; 35], or human dynamics in social networks [36], among others. However, although level sets [23] and density pruning techniques [29] are studied for visualization, to the best of our knowledge, three-dimensional (3D) spatiotemporal visualization, as in Figure 9, has not been exploited to date, whereas it can be very useful to locate different spatiotemporal events in the same management panel. In our system, the geographical representation was made over Google Maps, which can be readily handled with a publicly available function (\(plot\_google\_map\_m\)) that uses an API (Application Programming Interface) developed by the same company [37]. The map coordinates were stored in the WGS84 reference system [38]. These geographical coordinates were used to search an image of a bidimensional map to place the emergencies as visible points, as observed in Figure 2b. The map scale could be settled to adapt the represented area according to the search criteria for the analyzed events. Figure 8: Police emergencies by hours during 2014. Average of the 365 days of the year and their confidence intervals (CIs) are represented. Weekdays versus weekends emergencies can be seen with their variations. Figure 9: Spatiotemporal emergency slices for police during December (only \(11\) nonconsecutive days are illustrated for better visualization on page). It is easy to notice with this representation the variations in the geographical concentration of events during the month and its concentration over different regions of the city. Once the emergencies were placed over a reference map, we needed to identify the densest locations and represent these to create a heat map. With this purpose, a Parzen representation was applied, and some example results can be observed in Figure 4, where darker red areas correspond to a higher event density. In this case, a fixed bandwidth was used to yield a global (city-scale) view of emergencies in police, health, and transit services. We note that there is a noticeable similarity on the support for these three services, but the heat peaks are not always the same, as was the case for the time series peaks. For instance, police has a trimodal representation supported along the city, whereas health has a bimodal distribution, partially corresponding to that of the police, but with narrower main modes. On the other hand, transit events are distributed with strong multimodality, and their heat noticeably extends to the south-east, corresponding with one of the main roads that connects the city of Quito with the towns of Monjas, Conocoto and Sangolqui. In Figure 4d, we can observe Mariscal town on a short scale.