## 4 Experiments and Results
### Experiments on Synthetic Datasets  
This section analyzes the comparative tests with six other state-of-the-art algorithms on ten synthetic datasets. The original distributions of the synthetic datasets are shown in Figure 7a-j. In them, data points belonging to the same cluster are marked with the same color. In particular, Figure 7d,g exhibit uneven density characteristics, and datasets D31, S1, DS577, and T4.8K all feature indistinct cluster boundaries, especially D31 and S1. In order to clearly illustrate the experimental setup of each algorithm, Table 5 references the selection of parameters in the original paper for each algorithm and provides the experimental parameters on the synthetic dataset. Table 6 presents the ACC, ARI, and NMI results of each algorithm on different synthetic datasets to illustrate their performance. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset** & \multicolumn{1}{c}{**K-Means**} & **DBSCAN** & **DPC** & \multicolumn{1}{c}{**RNN-DBSCAN**} & **LDP-MST** & **HCDC** & \multicolumn{1}{c}{**CPDD-ID**} \\ \hline \multirow{3}{*}{Aggregation} & ACC & 0.78 & 0.98 & 0.99 & 0.99 & 0.99 & 0.99 & 0.99 \\  & NMI & 0.88 & 0.97 & 0.97 & 0.99 & 0.99 & 0.98 & 0.99 \\ \cline{1-1}  & ARI & 0.76 & 0.97 & 0.98 & 0.99 & 0.99 & 0.99 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The comparison of ACC, NMI, and ARI of 7 algorithms on synthetic datasets. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset** & \multicolumn{1}{c}{**K-Means**} & **DBSCAN** & **DPC** & \multicolumn{1}{c}{**RNN-DBSCAN**} & **LDP-MST** & **HCDC** & \multicolumn{1}{c}{**CPDD-ID**} \\ \hline Aggregation & k = 7 & EPS = 1.2, MinPts = 5 & dc = 2 & k = 14 & NC = 7 & NC = 7 & k = 11 \\ Spiral & k = 3 & EPS = 3, MinPts = 3 & dc = 2 & k = 7 & NC = 3 & NC = 3 & k = 3 \\ R15 & k = 15 & EPS = 0.3, MinPts = 3 & dc = 2 & k = 10 & NC = 15 & NC = 15 & k = 19 \\ Pathbased & k = 3 & EPS = 2, MinPts = 9 & dc = 3 & k = 6 & NC = 3 & NC = 3 & k = 6 \\ Jain & k = 2 & EPS = 2.5, MinPts = 15 & dc = 2 & k = 15 & NC = 2 & NC = 2 & k = 5 \\ D31 & k = 31 & EPS = 0.5, MinPts = 6 & dc = 2 & k = 13 & NC = 31 & NC = 31 & k = 29 \\ Zelink1 & k = 3 & EPS = 0.2, MinPts = 5 & dc = 3 & k = 14 & NC = 3 & NC = 3 & k = 6 \\ S1 & k = 15 & EPS = 197,500, MinPts = 2 & dc = 3 & k = 15 & NC = 15 & NC = 15 & k = 40 \\ DS577 & k = 3 & EPS = 0.45, MinPts = 5 & dc = 2 & k = 9 & NC = 3 & NC = 3 & k = 10 \\ T4.8K & k = 6 & EPS = 6, MinPts = 6 & dc = 2 & k = 14 & NC = 6 & NC = 6, w = 0.6 & k = 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal parameters of 7 algorithms on synthetic datasets. Figure 7: (a–j) show the original distributions of the ten synthetic datasets selected for the experiments. Figure 8 shows the clustering results of the proposed algorithm CPDD-ID on the synthetic datasets, where the results on popular datasets such as Spiral, Jain, and Zelink1 are consistent with the distribution of the original dataset, and the results on the three evaluation metrics are all 1. For datasets similar to D31, S1, and other datasets with a high degree of overlap between clusters, the CPDD-ID algorithm accurately separates clusters that do not belong to the same clusters that do not belong to the same category and also has good results in the evaluation metrics. Finally, the CPDD-ID algorithm also correctly recognizes different cluster structures when dealing with datasets with ambiguous boundaries such as Pathbased and DS577. Additionally, Figures 9-14 display the clustering results of the comparative algorithms DPC, DBSCAN, K-means, RNN-DBSCAN, LDP-MST, and HCDC on the ten synthetic datasets. It is worth noting that k-means shows the clustering centers detected on each dataset with a red pentagram, which is indicated by averaging the results over 30 runs on the experimental setup since variations in the initial parameters can lead to different results. Figure 9 presents the clustering results of DPC.