## 5 Results and Discussion
### Results
For each contamination rate, we generated an additional 1000 datasets, each of which included different values of coefficient \(a\). The results of this experiment are shown in Tables 7-9. As presented in Table 7, the LOF and EE algorithms keep the same type I error under different values of coefficient \(a\). The type I error of the IF algorithm is highly dependent on the value of coefficient \(a\). Therefore, the EE and LOF algorithms outperform the IF algorithm. Tables 7 and 8 indicate that the IF algorithm seems to have the highest type I and type II \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & & & & & & & & & & \\ \cline{2-10}
**Method** & \(m_{0}\) & **0.7** & **0.9** & **1.1** & **1.3** & & **1.5** & \\ \hline LOF & 20 & 0.995 & (0.016) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) \\ EE & & 0.993 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) \\ IF & & 0.580 & (0.180) & 0.853 & (0.082) & 0.935 & (0.043) & 0.970 & (0.034) & 0.983 & (0.025) \\ \hline LOF & 40 & 0.991 & (0.017) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) \\ EE & & 0.989 & (0.015) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) \\ IF & & 0.539 & (0.103) & 0.753 & (0.048) & 0.835 & (0.043) & 0.850 & (0.033) & 0.851 & (0.033) \\ \hline LOF & 60 & 0.984 & (0.017) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) \\ EE & & 0.988 & (0.016) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) & 1.000 & (0) \\ IF & & 0.504 & (0.070) & 0.641 & (0.046) & 0.690 & (0.046) & 0.699 & (0.032) & 0.703 & (0.032) \\ \hline \hline \end{tabular}  
Numbers in parentheses denote standard deviations.  
\end{table} 
Table 6: \(F_{2}\) score of the three outlier-detection algorithms under the assumption that the contamination rate is known. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \cline{2-10}
**Method** & \(m_{0}\) & **0.7** & **0.9** & **1.1** & **1.3** & & **1.5** & \\ \hline LOF & 20 & 0.005 & (0.016) & 0 & (0) & 0 & (0) & 0 & (0) & 0 & (0) \\ EE & & 0.008 & (0.018) & 0 & (0) & 0 & (0) & 0 & (0) & 0 & (0) \\ IF & & 0.260 & (0.070) & 0.100 & (0.058) & 0.055 & (0.037) & 0.025 & (0.035) & 0.015 & (0.024) \\ \hline LOF & 40 & 0.010 & (0.017) & 0 & (0) & 0 & (0) & 0 & (0) & 0 & (0) \\ EE & & 0.011 & (0.015) & 0 & (0) & 0 & (0) & 0 & (0) & 0 & (0) \\ IF & & 0.370 & (0.051) & 0.235 & (0.039) & 0.165 & (0.043) & 0.150 & (0.033) & 0.149 & (0.040) \\ \hline LOF & 60 & 0.017 & (0.018) & 0 & (0) & 0 & (0) & 0 & (0) & 0 & (0) \\ EE & & 0.012 & (0.016) & 0 & (0) & 0 & (0) & 0 & (0) & 0 & (0) \\ IF & & 0.440 & (0.029) & 0.345 & (0.038) & 0.300 & (0.039) & 0.303 & (0.031) & 0.288 & (0.027) \\ \hline \hline \end{tabular}  
\end{table} 
Table 5: Type II error of the three outlier-detection algorithms under the assumption that the contamination rate is known. errors and leads to an unsatisfactory \(F_{2}\) performance, as shown in Table 9. The results in Tables 7-9 indicate that the performance of the LOF and EE algorithms is not substantially affected by variations in the magnitudes of the outlier profiles. When the contamination rate is known, the type I errors of the three outlier-detection algorithms are lower than when the estimated contamination rate is used. This is because the type I error of the proposed method is a fixed value. With known contamination rates, while type I errors are significantly reduced, the type II errors of the three outlier-detection algorithms are also slightly increased. In all cases, the LOF and EE algorithms have quite close performance, and both substantially outperform the IF algorithm. This result can be attributed to the characteristics of profiles in the OOC state. In the future, different types of profiles and their anomaly types can be studied to compare the performance of various outlier-detection algorithms in further detail.