# Statistical Model for Mobile User Positioning Based on Social Information
## 4 Model Assessment
### Results  
The proposed method aims to solve the lack of the precise location of the users in the network, by means of exploiting the spatial context of both the connections and the scenario. The only way to obtain GPS measurements from the users is using the MDT functionality, which is rarely active and never to all the connections in the network. This missing information makes it impossible to estimate the error in the processing process, so a more exploratory evaluation is needed. For this, the results obtained with the proposed model are compared with the traditional E-CID method and an intermediate version, only adding the context dimension in the positioning. Thus, performance comparison assesses the inclusion of social data. First, a statistical comparison of the number of connections per tile is presented in Figure 5 and Table 3. Then, the spatial performance is checked in the two cases shown in Figure 4, to illustrate the resolution of the proposed method, in comparison to the other two models, presented in Figure 6.  
Figure 5 shows the number of connections per tile in the full scenario with a boxplot for the three models assessed (E-CID, context and social model). The ordinate axis is in logarithmic scale aiming to optimize the graphical representation. The figure illustrates how context and social models (i.e., those models using additional information) can improve user positions in the ring area. In particular, by adding the indoor context of the connections (i.e., context model), clusters of users are detected, thus emptying areas where there were no connections and, then, diminishing the amount of connections in those tiles widening statistical distribution in the figure compared to E-CID model. This is greatly enhanced by the inclusion of geopositioned posts from social networks (i.e., social model), which allows the identification of tiles with high connection  
Figure 5: Number of connections per tile by model. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Method** & **Minimum** & **25 th perc.** & **50 th perc.** & **75 th perc.** & **Maximum** \\ \hline E-CID model & \(1.79\times 10^{-4}\) & \(8.69\times 10^{-3}\) & \(3.60\times 10^{-2}\) & \(9.81\times 10^{-2}\) & 36.29 \\ Context model & \(4.06\times 10^{-5}\) & \(1.86\times 10^{-2}\) & \(4.87\times 10^{-2}\) & \(1.17\times 10^{-1}\) & 45.99 \\ Social model & \(1.82\times 10^{-6}\) & \(1.03\times 10^{-2}\) & \(3.03\times 10^{-2}\) & \(8.68\times 10^{-2}\) & 175.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of the number of connections per tile with the compared models. densities and unpopulated areas, masked in previous models. As a consequence, the statistical distribution for the social model is additionally widened. Moreover, and with the aim of checking the resolution for user distribution in the network, Figures 6-8 show, respectively, a heatmap with the number of connections per tile in the three E-CID, Context and Social models with high and low population densities each (i.e., six subfigures in three figures), presented previously in Figure 4.  
These figures highlight that the information provided by geolocated posts, when available, significantly improves the connection location process. Specifically, for high population density scenarios (Figures 5(a), 6(a) and 7(a)), where the activity in social networks is high enough to generate a significant number of geolocated publications, the social model achieves a significant increase for the resolution of connection distribution. Granularity for the social model (Figure 7(a)) is not observed in either E-CID or context models (Figures 5(a) and 6(a)). In contrast, context and social models behave similarly with a low population density (Figures 6(b) and 7(b)), due to the lack of geopositioned publications.