## 4 PER-SAC based Optimal Parameter Autotuning for DBSCAN
### PER-SAC Algorithm
PER-SAC-DBSCAN effectively improves the clustering accuracy of DBSCAN compared to K-Means and KANN by 12.84% and 5.03% in the average value of NMI, and by 12.07% and 12.97% in the average value of ARI, respectively. Compared to TD3-DBSCAN, PER-SAC-DBSCAN improves the average accuracy and stability of NMI by 1.19% and 85.71%, respectively. Although it has a slight loss by 1.13% in the average accuracy of ARI with TD3-DBSCAN, the stability of ARI is improved by 5.48%. Compared to SAC-DBSCAN, it improves the average accuracy of NMI and ARI by 1.68% and 0.07%, and the stability of both metrics by 57.14% and 1.37%, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**K-Means [4]**} & \multicolumn{2}{c}{**KANN [25]**} & \multicolumn{2}{c}{**TD3-DBSCAN [31]**} & \multicolumn{2}{c}{**SAC-DBSCAN [33]**} & \multicolumn{2}{c}{**PER-SAC-DBSCAN**} \\ \cline{2-11}  & **NMI** & **ARI** & **NMI** & **ARI** & **NMI** & **ARI** & **NMI** & **ARI** & **NMI** & **ARI** \\ \hline
1 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.776 & 0.678 & 0.8026 & 0.7005 & 0.8101 & 0.7174 \\
2 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.76 & 0.6549 & 0.8087 & 0.7186 & 0.8114 & 0.7212 \\
3 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.7632 & 0.6586 & 0.7935 & 0.6925 & 0.8114 & 0.7212 \\
4 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.794 & 0.6963 & 0.8121 & 0.7209 & 0.8077 & 0.7179 \\
5 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.7932 & 0.6955 & 0.8114 & 0.7212 & 0.8101 & 0.7174 \\
6 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.8121 & 0.7209 & 0.7958 & 0.6995 & 0.8039 & 0.7018 \\
7 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.78 & 0.6805 & 0.7698 & 0.6697 & 0.8117 & 0.7196 \\
8 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.76 & 0.6549 & 0.8085 & 0.7136 & 0.8121 & 0.7209 \\
9 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.8124 & 0.722 & 0.79 & 0.6925 & 0.7951 & 0.6937 \\
10 & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.7698 & 0.6697 & 0.7944 & 0.6969 & 0.7887 & 0.6876 \\ AVG & 0.6927 & 0.5242 & 0.6559 & 0.4994 & 0.782 & 0.6831 & 0.799 & 0.7026 & 0.806 & 0.7119 \\ STD & - & - & - & - & 0.019 & 0.024 & 0.012 & 0.015 & 0.008 & 0.012 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation results of parameter tuning algorithms with a 3.3K and 3-classfied dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**K-Means [4]**} & \multicolumn{2}{c}{**KANN [25]**} & \multicolumn{2}{c}{**TD3-DBSCAN [31]**} & \multicolumn{2}{c}{**SAC-DBSCAN [33]**} & \multicolumn{2}{c}{**PER-SAC-DBSCAN**} \\ \cline{2-11}  & **NMI** & **ARI** & **NMI** & **ARI** & **NMI** & **ARI** & **NMI** & **ARI** & **NMI** & **ARI** \\ \hline
1 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.783 & 0.6438 & 0.8377 & 0.7464 & 0.835 & 0.7397 \\
2 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8878 & 0.8344 & 0.8274 & 0.6623 & 0.8274 & 0.6673 \\
3 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.784 & 0.6463 & 0.8484 & 0.7617 & 0.8356 & 0.6697 \\
4 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8346 & 0.7473 & 0.783 & 0.6438 & 0.835 & 0.7397 \\
5 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8757 & 0.8188 & 0.8208 & 0.761 & 0.892 & 0.884 \\
6 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8759 & 0.8212 & 0.8829 & 0.8324 & 0.8312 & 0.6658 \\
7 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.783 & 0.6438 & 0.8866 & 0.8828 & 0.8812 & 0.8267 \\
8 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8634 & 0.8449 & 0.832 & 0.7358 & 0.8574 & 0.8051 \\
9 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8439 & 0.7542 & 0.783 & 0.6438 & 0.8312 & 0.6658 \\
10 & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.8474 & 0.7605 & 0.8375 & 0.7548 & 0.8518 & 0.7666 \\ AVG & 0.7515 & 0.663 & 0.8074 & 0.6577 & 0.838 & 0.7515 & 0.834 & 0.7425 & 0.848 & 0.743 \\ STD & - & - & - & - & 0.039 & 0.077 & 0.033 & 0.074 & 0.021 & 0.073 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Evaluation results of parameter tuning algorithms with an 8.5K and 5-classfied dataset.