## 5 Conclusions  
In this paper, a new clustering algorithm CPDD-ID is proposed, which combines both density-based and hierarchical clustering ideas. First, in order to cope with cluster structures with uneven densities and irregular shapes, a density-maxima-based delineation strategy is proposed, which utilizes kernel density estimation to compute the local density maxima and partition the subclusters using this coordinate as a benchmark. The proposed partitioning strategy accurately recognizes cluster structures with different density distributions and can overcome the problem of subclusters that do not belong to the same cluster but are close to each other being partitioned into one cluster. Second, a similarity metric focusing on the local neighborhood structure is proposed. This similarity metric iteratively merges the subclusters with the highest similarity generated in the division phase based on the degree of interaction between the shared k-nearest neighbors of the subclusters, which solves the problem of incorrectly merging subclusters that occurs in traditional hierarchical clustering algorithms when dealing with highly overlapping and interconnected cluster structures. The experimental results show that the CPDD-ID algorithm is applicable to more types of datasets and exhibits greater robustness compared to existing clustering algorithms, especially when dealing with datasets with uneven density and ambiguous boundaries, where it shows more competitive performance.  
Despite the fact that the proposed study has achieved some meaningful findings, there are still some limitations. The performance of the CPDD-ID algorithm is not optimal when dealing with the large number of redundant features present in high-dimensional datasets. In future work, in order to address the poor performance of the CPDD-ID algorithm on high-dimensional datasets, the goal is to propose a feature-selection algorithm to cope with the large amount of redundant information that exists in high-dimensional datasets. The proposed feature-selection algorithm should be able to select a representative subset of features that can improve the performance of the algorithm as well as maximize the representation of the original feature set.  
Conceptualization, Y.L., J.D., Y.D. and H.W.; methodology, Y.L.; software, H.W. and Y.D.; validation, Y.L., J.D., H.W. and Y.D.; formal analysis, Y.L., H.W. and Y.D.; investigation, H.W. and Y.D.; resources, Y.L.; data curation, H.W. and Y.D.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L. and J.D.; visualization, H.W. and Y.D.; supervision, J.D. All authors have read and agreed to the published version of the manuscript.  
This document is the result of the research project funded by the National Natural Science Foundation of China (62262034, 62262035).  
Not applicable.  
The publicly available datasets used in this study can all be found here [[https://github.com/Chelsea547/Clustering-Datasets](https://github.com/Chelsea547/Clustering-Datasets)]([https://github.com/Chelsea547/Clustering-Datasets](https://github.com/Chelsea547/Clustering-Datasets)) (accessed on 21 January 2025).  
The authors declare no conflicts of interest.