## 1 Introduction
The Density Peak Clustering (DPC) algorithm [18] stands out from other density clustering algorithms due to its ability to efficiently identify density peak points and cluster data of arbitrary shapes [19]. Moreover, it requires fewer parameters, making it well-suited for large-scale data clustering analysis. The algorithm holds significant research value and shows promising application prospects. However, there are several challenges associated with this algorithm, including its limited adaptability to high-dimensional data, manual selection of truncation distance and clustering centers, and potential privacy leakage during the clustering process. Consequently, many researchers have conducted studies on the DPC algorithm to address these issues. In response to the problem of distance convergence in the DPC algorithm for high-dimensional samples, [PERSON] et al. [20] proposed a novel density peak clustering algorithm for isolated nuclei and K-induction (IKDC), this algorithm addresses the issue by employing optimized isolation kernels to replace conventional distances. The new approach enhances the similarity between two samples in sparse domains, while reducing the similarity in dense domains. As a result, the convergence problem concerning distance measurements in high-dimensional samples is effectively resolved. To address the issue of manual selection of clustering centers in the DPC algorithm, numerous improved algorithms have been proposed by researchers. [PERSON] et al. [21] introduced a fast search density peak clustering algorithm based on a shared neighbor and adaptive clustering center algorithm (DPC-SNACC). This algorithm automatically determines the number of knee points in the decision graph by analyzing the characteristics of different datasets and eliminates the need for manual intervention in determining the number of clustering centers. Another approach was proposed by [PERSON] et al. [22], who developed a density peak clustering algorithm based on K-nearest neighbor and adaptive merge strategy (KNN-ADPC). This algorithm has only one parameter and performs clustering tasks automatically without human involvement. [PERSON] et al. [23] defined local density using a reasonable granularity principle, they introduced the concept of relative semantic distance to select clustering centers in the decision graph, resulting in a new density peak clustering method based on fuzzy semantic units. [PERSON] et al. [24] replaced local density with the local deviation of spatial distance in datasets with diverse structures. By generating a more reasonable clustering center decision graph, they defined a threshold to accurately classify and process low-density points, thus proposing the bias density peak clustering algorithm (DeDPC). This algorithm effectively identifies outliers among low-density points. Furthermore, [PERSON] et al. [25] introduced the principal density peak clustering algorithm (MDPC+), which rapidly detects the principal density peak in the peak graph. The principal density peak represents the highest density peak in the cluster. Based on the new central hypothesis, MDPC+ can easily detect the true center of multi-peak clustering scenarios. Moreover, [PERSON] et al. [26] proposed the density peak clustering algorithm based on natural adjacency and merge strategy (IDPC-NNMS). This algorithm identifies the natural neighborhood set of each data point and adaptively obtains its local density, effectively minimizing the influence of cutoff parameters on the final clustering result. Table 1 summarizes the applications and improvements of the clustering algorithm. In order to avoid the issue of privacy leakage during the clustering process in the DPC algorithm, researchers have proposed the integration of differential privacy techniques. Although there are limited studies on combining the DPC algorithm with differential privacy, some notable approaches have been introduced.