## 4 Results
### Data Set and Experimental Setup
#### 4.1.1 Simulation Log  
Firstly, by simulating event logs containing chaotic activities, the event logs before and after chaotic activity filtering can be compared to determine whether the filtering method can identify all chaotic activities in the logs and calculate the normal number of activities that need to be deleted from the logs if all randomly inserted activities are filtered out. In order to verify the accuracy of the chaotic activity filtering approach, first, in **step (1)**, a synthetic event log is generated from the process model to determine that there is no chaotic activity in the event log. Then, in **step (2)**, activities are manually inserted at random positions in the log. Due to the locations in these activity logs being randomly selected, it is assumed that these activities are chaotic. Change the number (\(k\)) of random positioning activities inserted to evaluate how chaotic activity filtering methods \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{2}{c}{_random(1)_} & \multicolumn{2}{c}{_random(2)_} & \multicolumn{2}{c}{_random(3)_} & \multicolumn{2}{c}{_random(4)_} & \multicolumn{2}{c}{_random(5)_} & \multicolumn{2}{c}{_random(6)_} & \multicolumn{2}{c}{_random(7)_} \\ \cline{2-13}  & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ \\ \hline \multirow{2}{*}{**Direct**} & 0 & 42 & 0 & 43 & 0 & 48 & 0 & 49 & 0 & 58 & 0 & 69 & 0 & 81 \\  & 0 & 51 & 0 & 54 & 0 & 56 & 0 & 60 & 0 & 66 & 0 & 75 & 0 & 82 \\  & 0 & 143 & 82 & 0 & 95 & 0 & 107 & 0 & 129 & 0 & 136 & 0 & 138 & 0 & 158 \\  & 0 & 86 & 0 & 103 & 0 & 113 & 0 & 129 & 0 & 142 & 0 & 165 & 0 & 178 \\  & 0 & 34 & \(0\) & 37 & \(0\) & _40_ & \(0\) & _46_ & \(0\) & _52_ & \(0\) & _58_ & \(0\) & _63_ \\  & 0 & 58 & \(0\) & 71 & \(0\) & _78_ & \(0\) & _92_ & \(0\) & _97_ & \(0\) & _109_ & \(0\) & _121_ \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of misdeletion rate of different filtering approach (Logs contain k uniform randomly-positioned activities) (ms). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{2}{c}{_frequent(1)_} & \multicolumn{2}{c}{_frequent(2)_} & \multicolumn{2}{c}{_frequent(3)_} & \multicolumn{2}{c}{_frequent(4)_} & \multicolumn{2}{c}{_frequent(5)_} & \multicolumn{2}{c}{_frequent(6)_} & \multicolumn{2}{c}{_frequent(7)_} \\ \cline{2-13}  & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ & _mdr_ & _time_ \\ \hline \multirow{2}{*}{**Direct**} & 0 & 44 & 0 & 48 & 0 & 56 & 0 & 60 & 0 & 68 & 0 & 73 & 0 & 88 \\
**Direct(\(\alpha\) = 1/ A1)** & 0 & 53 & 0 & 57 & 0 & 58 & 0 & 63 & 0 & 70 & 0 & 79 & 0 & 96 \\
**Indirect** & 0 & 89 & 0 & 105 & 0 & 114 & 0 & 126 & 0 & 138 & 0 & 156 & 0 & 168 \\
**Indirect(\(\alpha\) = 1/ A1)** & 0 & 96 & 0 & 111 & 0 & 120 & 0 & 136 & 0 & 153 & 0 & 172 & 0 & 184 \\
**Direct(\(df\))** & 0 & 35 & \(0\) & 39 & \(0\) & _45_ & \(0\) & _50_ & \(0\) & _57_ & \(0\) & _65_ & \(0\) & _71_ \\
**Indirect(\(df\))** & 0 & 62 & \(0\) & _78_ & \(0\) & _81_ & \(0\) & _104_ & \(0\) & _112_ & \(0\) & _113_ & \(0\) & _136_ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of misdeletion rate of different filtering approach (Logs contain k frequent randomly-positioned activities) (%) (ms).