## 5 Results and Discussion
### Results
The \(F_{2}\) scores of the LOF and EE algorithms are unaffected by the size of coefficient \(a\) and remain stable. The LOF algorithm has higher \(F_{2}\) scores than all the other algorithms; however, when the coefficient \(a\) increases, the \(F_{2}\) scores of other algorithms increase considerably. This result can be explained by the fact that as the coefficient \(a\) increases, the type II error decreases substantially, which results in a considerable increase in the \(F_{2}\) score. It is worth noting that when the coefficient \(a=0.7\), the \(F_{2}\) score of the MHD-C algorithm is considerably lower than that of the LOF and EE algorithms. However, when the coefficient \(a>0.7\), the \(F_{2}\) scores of the MHD-C algorithm are all close to the ideal value of 1.0. \begin{table}
\begin{tabular}{l 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 MHD-C & 20 & 0.792 & & 0.990 & & 1.000 & & 1.000 & & 1.000 & \\ PPOD & & 0.612 & & 0.892 & & 0.899 & & 0.892 & & 0.892 & \\ LOF & & 0.911 & (0.003) & 0.911 & (0.003) & 0.912 & (0.003) & 0.912 & (0.003) & 0.912 & (0.003) \\ EE & & 0.909 & (0) & 0.909 & (0) & 0.909 & (0) & 0.909 & (0) & 0.909 & (0) \\ IF & & 0.773 & (0.061) & 0.909 & (0) & 0.909 & (0) & 0.909 & (0) & 0.909 & (0) \\ \hline MHD-C & 40 & 0.944 & & 0.994 & & 1.000 & & 1.000 & & 1.000 & \\ PPOD & & 0.522 & & 0.948 & & 0.950 & & 0.950 & & 0.950 & \\ LOF & & 0.962 & (0.001) & 0.962 & (0.001) & 0.963 & (0.002) & 0.963 & (0.002) & 0.963 & (0.002) \\ EE & & 0.962 & (0) & 0.962 & (0) & 0.962 & (0) & 0.962 & (0) & 0.962 & (0) \\ IF & & 0.664 & (0.041) & 0.841 & (0.041) & 0.869 & (0.037) & 0.893 & (0.030) & 0.898 & (0.024) \\ \hline MHD-C & 60 & 0.962 & & 0.997 & & 0.999 & & 1.000 & & 0.999 & \\ PPOD & & 0.316 & & 0.970 & & 0.971 & & 0.971 & & 0.971 & \\ LOF & & 0.979 & (0.005) & 0.981 & (0.001) & 0.981 & (0.001) & 0.981 & (0.001) & 0.981 & (0.001) \\ EE & & 0.979 & (0.004) & 0.980 & (0) & 0.980 & (0) & 0.980 & (0) & 0.980 & (0) \\ IF & & 0.590 & (0.039) & 0.688 & (0.035) & 0.729 & (0.035) & 0.726 & (0.035) & 0.750 & (0.035) \\ \hline \hline \end{tabular} Numbers in parentheses denote standard deviations.  
\end{table} 
Table 3: \(F_{2}\) score of each considered method under different estimated contamination rates and different magnitudes of coefficient \(a\). The variation in the performance of the MHD-C algorithm may be attributed to the method of performance evaluation. The adopted evaluation framework is based on the assumption that there is only one size of coefficient \(a\) in each dataset. However, in practical applications, each collected dataset may contain a variety of outlying profiles with different sizes of coefficient \(a\), and this affects the estimation of type I and type II errors. Another interesting observation is that the performance of the PPOD and IF algorithms is similar. When the coefficient \(a\) is equal to 0.7, the \(F_{2}\) scores of both methods are very low, but as the coefficient \(a\) increases, their \(F_{2}\) scores stabilize. As the contamination rate increases, the \(F_{2}\) scores of the LOF and EE algorithms increase. This indicates that the LOF and EE algorithms have lower false negative rates. However, the \(F_{2}\) scores of the PPOD and IF algorithms decrease with an increase in the contamination rate. The \(F_{2}\) score of the LOF algorithm is marginally higher than that of the EE algorithm, and these algorithms have similar type I and type II errors. The \(F_{2}\) score of the IF algorithm is substantially lower than those of the other algorithms. In the above comparisons, type I and type II errors were assessed separately for different parameters \(a\). This evaluation method does not quite match the situation of practical application. The dataset collected in SPC phase I usually contains normal profiles and outlying profiles of various variation sizes (different parameter \(a\)).