## 6 Experiments
### Selecting Background Knowledge Configurations with Low-Entropy Feature Frequency
#### 6.5.1 Wi-Fi  
In the next experiments, we explored the analysis of the Wi-Fi dataset, which offers data on user mobility based on Wi-Fi access point connections. Our primary objective was to assess the distribution of re-identification risk and evaluate the potential impact of targeting low-entropy and feature frequency in background knowledge configurations. Specifically, we aimed to determine whether significant computational savings were achievable by employing a reduced method if the risk assessment distributions remained comparable between the conventional and reduced approaches. By conducting this analysis, we aimed to improve the efficacy by leveraging specific features such as location and time to enhance privacy risk assessment in Wi-Fi-based trajectory data. Through detailed examination and comparison of risk distributions, we aimed to determine the feasibility and benefits of optimizing the risk assessment process while maintaining the integrity of privacy protection mechanisms. In Tables 1 and 2, the first line compares re-identification risk distributions using location frequency and lower entropy to reduce the background knowledge set with the standard approach (knowledge size = 1). In Table 1, low \(p\)-values suggest significant differences in re-identification risk distributions for the location sequence attack. Conversely, lower Ks-statistics values, in Table 2, represent a similar distribution. We used both measures to analyze the similarity of the distributions. Configurations with low-entropy locations in the Wi-Fi dataset with a knowledge size equal to 1 and the location sequence attack may not accurately represent associated risk levels when selecting only part of the instances. Only considering location with low entropy frequency would not represent the correct risk value when the knowledge size is 1. We can also notice that, as the percentage of low-entropy and location frequency increases from 10% to 50%, the \(p\)-values increase, suggesting a higher degree of similarity between risk assessments. It also means that we cannot represent the risk using small percentage values. The second line in Table 1 provides \(p\)-values for the location sequence attack, comparing approaches using location as a feature, considering a knowledge value of \(k=2\). The \(p\)-values indicate the statistical significance of differences in re-identification risk distributions between the standard and lower entropy/location frequency reduced background knowledge set. For the location sequence attack, the \(p\)-values are relatively high, especially at higher percentages of knowledge, suggesting a lack of significant differences in risk distributions. \(p\)-values close to 1 indicate that the distributions are not very different. The third line in Table 1 presents \(p\)-values for the visiting attack, comparing approaches using location as a feature with a knowledge value of \(k=1\). The \(p\)-values are closer to 0 than 1, indicating a significant difference between risk assessments using reduced combinations and those using the original formula considering all background knowledge. As the percentage of low entropy and location frequency increases from 10% to 50%, the \(p\)-values also increase, suggesting a higher degree of similarity between risk assessments. This implies that we cannot accurately represent the risk using a few values and low-entropy location frequency alone. The Ks-statistics, in Table 2, presents the same results as discussed for \(p\)-values. We have high statistics values, which means that the distributions are different, and the percentage of low entropy decreases in the past, and the percentage value increases. Background knowledge configurations targeting low-entropy locations in the Wi-Fi dataset with a knowledge size of 1 and the visiting attack may not accurately represent the associated risk levels when selecting only some instances. In this case, another feature (or combinations of features) is likely responsible for the uniqueness of the background knowledge set.