## 1 Introduction
[PERSON] incorporated the concept of reachable center points into the DPC algorithm and proposed DP-rcCFSFDP [27], which combines differential privacy technology. This approach achieves good clustering results. However, this algorithm still faces challenges such as subjective truncation distance and clustering center selection, as well as limited applicability to high-dimensional data. [PERSON], [PERSON], et al. proposed a DPC algorithm for differential privacy protection based on \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Solved Problems** & **Proposed Algorithm** & **Characteristics** \\ \hline \multirow{4}{*}{[PERSON] et al. [18]} & To make it easier to & \multirow{4}{*}{A novel density peaks clustering algorithm with isolation kernel and K-induction (IKDC)} & \multirow{4}{*}{It is superior to other algorithms} \\  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \multirow{4}{*}{[PERSON] et al. [22]} & To solve the subjectivity & \multirow{4}{*}{A density peak clustering algorithm based on K nearest neighbors with adaptive merging strategy (KNN-ADPC)} & \multirow{4}{*}{Higher accuracy of KNN-ADPC compared with DBSCAN, K-means++, DPC, and DPC-KNN.} \\  & of determining cluster centers & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \multirow{4}{*}{[PERSON] et al. [23]} & To improve the & \multirow{4}{*}{A novel method for density peaks clustering based on fuzzy semantic cells} & \multirow{4}{*}{Exhibits higher performance} \\  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \multirow{4}{*}{[PERSON] et al. [25]} & To overcome the bad & \multirow{4}{*}{A Main Density Peak Clustering algorithm (MDPC+)} & \multirow{4}{*}{Suitable for large datasets, superior in detecting center detection} \\  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \multirow{4}{*}{[PERSON] et al. [26]} & To solve DPC algorithm works poorly on & \multirow{4}{*}{An improved density peaks clustering algorithm based on natural neighbor with a the effectiveness and superiority} \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The summarization of the applications and improvements of the clustering algorithm. shared neighbor similarity DP-DPCSNNS [28]. This algorithm computes the local density of samples by combining shared neighbor similarity with Euclidean distance and utilizes shared neighbor similarity to detect clustering centers. This methodology facilitates the selection of appropriate clustering centers. [PERSON] et al. proposed two improved density peak clustering algorithms based on differential privacy [29; 30] with distinct perspectives. These approaches address various challenges, including weak clustering effects on high-dimensional datasets, manual selection of clustering centers and truncation distances, as well as privacy leakage during the clustering analysis in the DPC algorithm. Table 2 summarizes the application of differential privacy techniques to clustering algorithms. Building upon these studies, this paper proposes an improved DPC algorithm based on Chebyshev inequality and differential privacy called DP-CDPC from the perspective of the decision graph. The flowchart of the DP-CDPC algorithm is shown in Figure 1.  
The specific contributions are as follows:  
1. Aiming at the problem of manual selection of clustering centers in the traditional DPC algorithm, different from DP-ADPC proposed in the literature [29], this paper proposes an improved DPC algorithm based on Chebyshev inequality (CDPC). From the perspective of the decision graph, CDPC constructs constraint conditions for the statistics of the decision graph using Chebyshev inequality. By adjusting the parameters of the algorithm, the threshold of the statistics is determined, and CDPC automatically identifies the clustering centers. 2.