## 4 Experiments and Results
### Experiments on Synthetic Datasets
DPC is applied to various datasets by setting different truncation distances and gives good results on spherical datasets. It can be seen that it performs well on datasets such as R15 but performs poorly on datasets with uneven density such as Pahbased and Jain. The clustering results of DBSCAN are shown in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & \multicolumn{1}{c}{**K-Means**} & **DBSCAN** & **DPC** & \multicolumn{2}{c}{**RNN-DBSCAN**} & **LDP-MST** & **HCDC** & \multicolumn{1}{c}{**CPDD-ID**} \\ \hline \multirow{3}{*}{Spiral} & ACC & 0.34 & 1 & 1 & 1 & 1 & 1 & 1 \\  & NMI & 0.001 & 1 & 1 & 1 & 1 & 1 & 1 \\  & ARI & \(-\)0.005 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{R15} & ACC & 0.71 & 0.91 & 0.97 & 0.97 & 0.99 & 0.99 & 0.99 \\  & NMI & 0.87 & 0.90 & 0.95 & 97 & 0.99 & 0.98 & 0.99 \\  & ARI & 0.69 & 0.85 & 0.94 & 0.97 & 0.99 & 0.98 & 0.99 \\ \hline \multirow{3}{*}{Pathbased} & ACC & 0.74 & 0.98 & 0.72 & 0.98 & 0.67 & 0.56 & 0.99 \\  & NMI & 0.54 & 0.96 & 0.51 & 0.93 & 0.49 & 0.59 & 0.98 \\  & ARI & 0.46 & 0.98 & 0.44 & 0.95 & 0.41 & 0.45 & 0.99 \\ \hline \multirow{3}{*}{Jain} & ACC & 0.78 & 0.89 & 0.92 & 0.99 & 1 & 1 & 1 \\  & NMI & 0.37 & 0.79 & 0.64 & 0.95 & 1 & 1 & 1 \\  & ARI & 0.32 & 0.79 & 0.69 & 0.98 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{D31} & ACC & 0.78 & 0.85 & 0.96 & 0.91 & 0.97 & 0.86 & 0.96 \\  & NMI & 0.95 & 0.87 & 0.94 & 0.95 & 0.96 & 0.93 & 0.94 \\  & ARI & 0.82 & 0.69 & 0.92 & 0.89 & 0.94 & 0.84 & 0.91 \\ \hline \multirow{3}{*}{Zelink1} & ACC & 1 & 1 & 0.46 & 1 & 1 & 1 & 1 \\  & NMI & 1 & 1 & 0.17 & 1 & 1 & 1 & 1 \\  & ARI & 1 & 1 & 0.06 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{S1} & ACC & 0.82 & 0.97 & 0.99 & 0.98 & 0.99 & 0.73 & 0.99 \\  & NMI & 0.93 & 0.96 & 0.98 & 0.98 & 0.99 & 0.90 & 0.98 \\  & ARI & 0.82 & 0.96 & 0.98 & 0.97 & 0.99 & 0.70 & 0.98 \\ \hline \multirow{3}{*}{DS577} & ACC & 0.98 & 0.99 & 0.99 & 0.99 & 0.99 & 0.99 & 0.99 \\  & NMI & 0.94 & 0.98 & 0.97 & 0.97 & 0.99 & 0.98 & 0.99 \\  & ARI & 0.96 & 0.99 & 0.98 & 0.98 & 0.99 & 0.99 & 0.99 \\ \hline \multirow{3}{*}{T4.8K} & ACC & 0.64 & 0.98 & 0.73 & 0.90 & 0.91 & 0.65 & 0.89 \\  & NMI & 0.52 & 0.97 & 0.66 & 0.86 & 0.86 & 0.47 & 0.85 \\ \cline{1-1}  & ARI & 0.61 & 0.95 & 0.74 & 0.86 & 0.87 & 0.69 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._Figure 8: (a-j) show the clustering results of the CPDD-ID algorithm on ten synthetic datasets. Figure 10: (a–j) show the clustering results of the DBSCAN algorithm on ten synthetic datasets. Figure 9: (a–j) show the clustering results of the DPC algorithm on ten synthetic datasets. DBSCAN can handle datasets of arbitrary shapes, and it especially excels in handling datasets such as Jain and Zelink1 that have clear cluster structures and are far away from each other. However, it incorrectly categorizes clusters close to each other as one cluster when dealing with datasets such as R15, S1, etc., which have unclear inter-cluster structures and are highly overlapping. As shown in Figure 11, K-means performs well on the Zelink1 dataset but performs poorly on Aggregation, Spiral and Pathbased, incorrectly classifying different clusters together and even detecting the wrong cluster centers. It also performs poorly on noisy datasets such as T4.8k. RNN-DBSCAN is a density-based clustering algorithm based on DBSCAN that uses reverse nearest neighbors to compute the local density, and it shows better clustering performance than DBSCAN, as shown in Figure 12.  
Especially on the Jain and Aggregation datasets, the potential cluster structure is correctly identified. However, it is not as good as DBSCAN in dealing with datasets containing noise like T4.8k. Moreover, the RNN-DBSCAN algorithm is not suitable for datasets with ambiguous boundaries such as R15, D31, and Pathbased. Figure 11: (**a-j**) show the clustering results of the K-means algorithm on ten synthetic datasets. Figure 12: (**a-j**) show the clustering results of the RNN-DBSCAN algorithm on ten synthetic datasets.