## 4 Experiments and Results
### Parameter Analysis of Algorithms  
To verify the effect of the shared nearest neighbor parameter \(K\) on the performance of the CPDD-ID algorithm, a further analysis was performed on the synthetic dataset. This analysis deflates the range of \(K\) values from 1 to 50, and Figure 15 demonstrates the effect of the variation of the parameter \(K\) on the ACC, NMI, and ARI scores.  
It can be seen that the results on the Aggregation dataset smooth out as the value of \(K\) increases, remaining constant especially in the range of 11 to 33 and showing a downward trend when the value of \(K\) is greater than about 43. The Spiral dataset shows a decreasing and then stabilizing trend. There is a small fluctuation on the Pathbased dataset. There is also a stabilizing effect on DSS57, which is a dataset with uneven density. In particular, the CPDD-ID algorithm performs very smoothly and well on datasets with ambiguous and highly overlapping boundaries such as R15, D31, and S1, which shows that the CPDD-ID algorithm is effective in dealing with this type of dataset.  
On the basis of the above analysis, we suggest that the k value be set within the range of [5,12] when dealing with datasets such as Spiral, Jain, and Pathbased, which have a streaming structure. This is because there are generally many localized density peaks in such datasets, which may be partitioned into multiple subclusters during division, and if the k value is too large, it may incorrectly merge subclusters that do not belong to the same cluster structure. In addition, for datasets such as Aggregation, R15, D31, and S1, which have highly overlapping and interconnected clusters, the only way to avoid having highly overlapping cluster structures being incorrectly merged is to scale up the evaluation of the number of shared k-nearest neighbors. In addition, smaller k values tend to merge some clusters that do not belong to a cluster but are connected by a small number of samples into a single cluster. Therefore, a k value of [10,25] is recommended for such datasets.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & **K-Means** & **DBSCAN** & **DPC** & \
\begin{tabular}{c} **RNN-** \\ **DBSCAN** \\ \end{tabular} &
\begin{tabular}{c} **LDP-** \\ **MST** \\ \end{tabular} & **HCDC** & **CPDD-ID** \\ \hline \multirow{3}{*}{Satimage} & ACC & 0.64 & 0.39 & 0.69 & 0.24 & 0.58 & 0.32 & 0.76 \\  & NMI & 0.61 & 0.30 & 0.61 & 0.001 & 0.61 & 0.28 & 0.58 \\  & ARI & 0.52 & 0.04 & 0.54 & 0.00 & 0.44 & 0.09 & 0.57 \\ \hline \multirow{3}{*}{Yeast} & ACC & 0.17 & 0.32 & 0.28 & 0.32 & 0.25 & 0.28 & 0.32 \\  & NMI & 0.01 & 0.01 & 0.01 & 0.001 & 0.01 & 0.01 & 0.02 \\  & ARI & 0.01 & 0.002 & \(-\)0.005 & 0.002 & 0.003 & 0.006 & 0.005 \\ \hline \multirow{3}{*}{Balance} & ACC & 0.04 & 0.005 & 0.46 & 0.47 & 0.47 & 0.47 & 0.56 \\  & NMI & 0.01 & 0.25 & 0.06 & 0.02 & 0.03 & 0.008 & 0.13 \\  & ARI & 0.002 & 0.14 & 0.02 & 0.01 & 0.02 & \(-\)0.001 & 0.15 \\ \hline \multirow{3}{*}{Breast} & ACC & 0.95 & 0.90 & 0.00 & 0.66 & 0.95 & 0.59 & 0.95 \\  & NMI & 0.73 & 0.62 & 0.00 & 0.005 & 0.72 & 0.06 & 0.70 \\ \cline{1-1}  & ARI & 0.83 & 0.65 & 0.00 & 0.003 & 0.82 & \(-\)0.04 & 0.81 \\ \hline \hline \end{tabular}
\end{table}
Table 8: _Cont._Figure 15: (**a**–**h**) show the trend of the parameter \(K\) value in the CPDD-ID algorithm on the synthetic dataset for ACC, NMI, and ARI. (The blue folds are ACC, the orange folds are NMI, and the green folds are ARI.)