# A Goal-Oriented Evaluation Methodology for Privacy-Preserving Process Mining
## 4 Case Study
### PPPM Analysis and the Derivation of Answers to Questions
#### 4.5.8 PPPM Analysis of DP-k-Means (Q2.1.3)  
In this section, we present the quantitative results of applying the DP-k-Means model on our real-life event logs under two different aspects as result and time utility qualities. In  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Event Log** & **Epsilon = 0.01** & **Epsilon = 0.05** & **Epsilon = 0.1** & **Epsilon = 0.5** & **Epsilon = 1** \\ \hline Sepsis & 0.16942 & 0.14447 & 0.14175 & 0.14023 & 0.14360 \\ BPIC13 & 0.57645 & 0.60080 & 0.60019 & 0.58835 & 0.57865 \\ CoSeLog & 0.084728 & 0.0082668 & 0.078429 & 0.081888 & 0.0084339 \\ Road Traffic Fines & 5.1188 & 5.1623 & 5.1640 & 5.0518 & 5.1361 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Discovered DP-Decision Trees model runtime(s) metric results.  
Figure 16: Discovered Decision Trees before and after DP-privacy for Road Traffic Fines event log.  
Figure 15: Discovered DP-Decision Trees model quality results.  
order to create a baseline for our comparisons, Table 8 includes both the metric values of model quality and runtime performances as a result of applying the naive (non-private) version of the k-Means clustering model on four different real-life event logs.  
Result Utility Quality  
Figure 17 shows the DP-k-Means clustering model inertia (min-max scaled) metric with respect to the epsilon parameter values behavior on our real-life event logs. For each event log, the values show an expected decreasing trend compared with the baseline non-private values due to the anonymized nature. However, for the CoSeLog and Road Traffic Fines event logs, there exist small deviations between the two epsilon values due to the nondeterministic property of differential privacy.  
Time Utility Quality  
Table 9 includes the runtime(s) performance metric results of the applied DP-k-Means clustering model on our real-life event logs. Based on the results, an increase in the uniqueness of traces within the event logs corresponds to a more significant reduction in the model runtime performance. Thus, these kind of event logs are more suitable for differential privacy-preserving clustering techniques in terms of time performance consideration. Furthermore, a rapid clustering process does not necessarily guarantee precisely accurate representative selection.  
Figure 17: Discovered DP-k-Means clustering model quality results.  
\begin{table}
\begin{tabular}{l c c c} \hline
**Event Log** & **Inertia Value** & **Time** \\ \hline Sepsis & 1,375,898,051,000 & 0.650 \\ BPIC13 & 1,157,175,781,977.000 & 0.520 \\ CoSeLog & 749,964,802.000 & 0.710 \\ Road Traffic Fines & 7,249,390,361,712.000 & 11.400 \\ \hline \end{tabular}
\end{table}
Table 8: Discovered (non-private) k-Means clustering model quality and runtime metric (s) results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Event Log** & **Epsilon = 0.01** & **Epsilon = 0.05** & **Epsilon = 0.1** & **Epsilon = 0.5** & **Epsilon = 1** \\ \hline Sepsis & 0.580 & 0.530 & 0.520 & 0.500 & 0.480 \\ BPIC13 & 0.310 & 0.320 & 0.310 & 0.310 & 0.300 \\ CoSeLog & 0.210 & 0.220 & 0.210 & 0.190 & 0.200 \\ Road Traffic Fines & 2.170 & 2.180 & 2.160 & 5.370 & 6.230 \\ \hline \end{tabular}
\end{table}
Table 9: Discovered DP-k-Means clustering model runtime(s) metric results.