## 6 Experiments
### Selecting Background Knowledge Configurations with Low-Entropy Feature Frequency
#### 6.5.1 Wi-Fi
When we increase the percentage value, which means that we are considering possible low-entropy time values in the background knowledge, the \(p\)-values go up because there are more chances of selecting sets with high risk. The same observations can be seen with statistics values, the values close to 1 showing the difference in the distributions. When we increase the percentage value, the statistics values get closer to 0. Table 1's last line shows \(p\)-values for a visit attack, comparing approaches, and considering different percentages and knowledge size 2 for the background knowledge configuration. In all scenarios presented in the table, the \(p\)-values are consistently 1. This suggests that, regardless of the knowledge percentage used, there is no statistically significant difference in the distributions of re-identification risk between standard time values and lower entropy time values. The same can be observed in statistics values, where all values are very close to 0, meaning that the distributions are almost identical. The overall analysis shows that, as the \(k\) size increases, the likelihood of encountering more unique values also grows. Furthermore, the applicability of the lower entropy shortcut is possible based on the uniqueness of the feature. This shortcut proves useful when dealing with features characterized by many unique values distributed across trajectories. Specifically, in the Wi-Fi dataset, where spatial and temporal data are densely populated due to numerous individuals connecting simultaneously within a confined area, the time and location information, when considered separately, tend to be less unique, as can be seen in Figure 4, especially for small knowledge sizes. This dataset's uniqueness arises from locations representing access points where multiple individuals can connect simultaneously. However, what truly distinguishes behaviors is the sequence of events of locations and time. Table 3 shows that the **Low-Entropy Percentile** approach significantly reduces execution times for attacks on location and time features compared with the **Original**. For location visit attacks (\(k=1\)), execution times drop from 2314 days to between 333 and 1265 days, and, for \(k=2\), from 60,395 days to between 16,147 and 48,221 days. For time visit attacks (\(k=1\)), times decrease from 2300 days to between 279 and 1183 days, and, for \(k=2\), from 66,150 days to between 14,333 and 50,564 days. The reductions are more substantial for visit attacks than for location sequence attacks. The **Break** and **Low-Entropy Percentile** approach consistently reduces execution times for all attack types compared to the **Break** method. Table 4 shows that, for location visit attacks (\(k=1\)), times drop from 141 days to between 117 and 132 days, and, for \(k=2\), from 420 days to between 261 and 375 days. For time visit attacks (\(k=1\)), times decrease from 141 days to between 116 and 131 days, and, for \(k=2\), from 460 days to between 276 and 393 days. Location sequence attacks (\(k=1\)) show reductions from 20 days to between 3 and 11 days, and, for \(k=2\), from 2224 days to between 679 and 1787 days.