## 2 Related Work  
### Density Peak Clustering Algorithm  
The DPC algorithm is a density-based clustering algorithm published in 2014, which is widely used in various scenarios and achieved good results according to the two core ideas of clustering centers with high local density and centers with different local densities that have a long distance. The clustering centers of the DPC algorithm can be selected manually based on the decision map, which contains two important attributes: the local density is represented on the horizontal axis, while the vertical coordinate indicates relative distance, the allowing identification of density peaks and outliers. In addition, its data point allocation strategy is based on single-chain label propagation, which assigns data points to those with the highest local density of nearest neighbors based on the nearest-neighbor principle. In recent years, density-based clustering algorithms have gradually become mainstream. For example, [PERSON] et al. [14] proposed a density-based clustering algorithm called the density-based clustering algorithm using reverse nearest neighbor density estimates (RNN-DBSCAN) based on DBSCAN, which uses inverse nearest neighbors to estimate the local density and traverses the data points based on the k-nearest neighbor graph. Compared to the DBSCAN algorithm, it uses only one parameter (k-nearest neighbors) to estimate the density, and secondly, it also demonstrates superiority in dealing with variable-density datasets but performs poorly on datasets with ambiguous boundaries. [PERSON] et al. proposed a clustering algorithm called the local density peak and minimum spanning tree clustering algorithm (LDP-MST) [15], which utilizes the minimum spanning tree and the density peak. It constructs a minimum spanning tree using local density peaks and then iteratively splits the longest edges until the termination condition is reached, which is robust to datasets with complex structures. [PERSON] et al. [16] integrated the idea of nearest-neighbor graphs into DPC, which calculates the local densities and distances through an improved mutual k nearest-neighbor graph and uses the two assumptions of DPC to constrain and select the clustering centers. The proposed algorithm can ensure the correct selection of suitable clustering centers and effectively improve the clustering performance. [PERSON] et al. [17] calculation the local density and relative distance based on the natural neighbors to classify the subclusters, which can effectively eliminate the effect of cutoff parameters on the clustering results. Then, a novel merging strategy is utilized to merge the subclusters generated in the division stage until the termination condition is satisfied. Euclidean distance, a commonly used distance metric for density clustering algorithms, is widely used, but it ignores the contribution of individual features to the similarity and clustering of data points. In order to address this limitation, [PERSON] et al. pro posed standard deviation weighted distance and fuzzy weighted k-nearest neighbor-based density peak clustering (SFKNN-DPC) [18], which enhances the Euclidean distance by utilizing the standard deviation-weighted distances, and this strategy takes into account the specific contribution of each individual feature to the similarity between data points. To address clustering with multiple density peaks, [PERSON] et al. [19] proposed an effective data relevance measure based on probability mass named the density peak clustering algorithm based on probability mass (MP-DPC) and integrated it into the DPC algorithm. To avoid the domino effect inherent in the DPC's single-allocation strategy, where an error in assigning one point leads to the misallocation of other data points, [PERSON] et al. [20] utilized label propagation and the Jaccard coefficient to propose a two-step allocation strategy for measuring the similarity between data points, which is concerned only with the k points of highest similarity.