## 4 Experimental Results and Analysis
### Analysis of Algorithm Results
#### 4.3.1 Synthetic Datasets  
According to the parameter settings of each algorithm in different datasets in Table 4, the effectiveness of each algorithm on synthetic datasets is shown in Table 5; the bolded values in the table represent the optimal experimental results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**DBSCAN**} & \multicolumn{2}{c}{**DP-ADPC**} & \multicolumn{2}{c}{**DP-CDPC**} \\ \cline{2-7}  & \(eps\) & \(mpts\) & \(p\) & \(\varepsilon\) & \(\varepsilon\) & \(b_{1}\) & \(b_{2}\) \\ \hline flame & 0.4 & 10 & 3 & 16 & 15 & 3 & 1 \\ spiral & 0.4 & 1 & 2 & 24 & 24 & 3 & 1 \\ compound & 0.4 & 19 & 6 & 18 & 1.5 & 3 & 0.5 \\ aggregation & 0.4 & 1 & 4 & 3 & 2 & 1 & 0.5 \\ R15 & 0.4 & 1 & 4 & 6 & 3 & 3 & 0.5 \\ D31 & 0.01 & 1 & 1 & 2 & 0.5 & 2 & 0.5 \\ seeds & 1.2 & 17 & 0.9 & 5 & 4 & 2 & 1 \\ ecoli & 0.8 & 4 & 0.1 & 4.5 & 0.5 & 2 & 0.5 \\ movement & 2.8 & 1 & 0.1 & 2 & 1 & 1 & 0.5 \\ dermatology & 4 & 4 & 0.1 & 5 & 0.5 & 3 & 0.5 \\ banknote & 0.4 & 4 & 2.5 & 2 & 1 & 3 & 1 \\ abalone & 0.4 & 19 & 2.9 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter settings. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Algorithm** & \(ARI\) & \(AMI\) & \(FMI\) \\ \hline \multirow{8}{*}{flame} & K-means & 0.409 & 0.368 & 0.715 \\  & DBSCAN & 0.934 & 0.866 & 0.969 \\  & SNNDPC & 0.950 & 0.911 & 0.977 \\  & ADPC & **1.000** & **1.000** & **1.000** \\  & CDPC & **1.000** & **1.000** & **1.000** \\  & DP-ADPC & 0.966 & 0.968 & 0.983 \\  & DP-CDPC & 0.970 & 0.970 & 0.990 \\ \hline \multirow{8}{*}{spiral} & K-means & \(-0.006\) & \(-0.005\) & 0.328 \\  & DBSCAN & **1.000** & **1.000** & **1.000** \\  & SNNDPC & **1.000** & **1.000** & **1.000** \\  & ADPC & **1.000** & **1.000** & **1.000** \\  & CDPC & **1.000** & **1.000** & **1.000** \\  & DP-ADPC & 0.850 & 0.853 & 0.901 \\  & DP-CDPC & 0.885 & 0.885 & 0.923 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The clustering evaluation index of each algorithm for synthetic datasets. As can be seen from Table 5, for the flame dataset, the clustering result of the CDPC and ADPC are same, and they achieve higher values for all three external evaluation indexes compared to other algorithms. After adding noise, the evaluation values slightly decrease but remain higher than other algorithms. Moreover, the DP-CDPC algorithm outperforms the DP-ADPC algorithm in terms of external evaluation indexes. In the case of the spiral dataset, the CDPC, DBSCAN, SNNDPC, and ADPC algorithms all achieve optimal values for each clustering evaluation index, namely, \(ARI\), \(AMI\), and \(FMI\) all reaching 1. These algorithms exhibit superior clustering effects compared to the K-means algorithm. The values of \(ARI\), \(AMI\), and \(FMI\) for the DP-CDPC algorithm are 0.8845, 0.8851, and 0.9232, respectively, which are larger than those of the DP-ADPC algorithm. However, compared to the CDPC algorithm, the clustering effect of the DP-CDPC algorithm shows a significant reduction. For dataset compound, \(ARI\) of the DBSCAN is larger than other algorithms, while \(AMI\) and \(FMI\) of the CDPC and ADPC are the same and larger than other algorithms. The evaluation indexes of the DP-ADPC and DP-CDPC are slightly lower than the ADPC and CDPC, but still higher than the other three algorithms in general, while the indexes of the DP-ADPC are slightly smaller than those of the DP-CDPC. For dataset aggregation, the clustering effect of the ADPC and CDPC is consistent and superior to the K-means, DBSCAN, and SNNDPC, while the clustering evaluation indexes of the DP-ADPC and DP-CDPC are slightly lower than the CDPC, but still higher than the others. Furthermore, the DP-CDPC algorithm exhibits a better effect than the DP-ADPC algorithm. In the case of the R15 dataset, all the values of the evaluation indexes of each algorithm are the same, except for the DBSCAN algorithm, and larger than that of the DBSCAN algorithm.