# Hybrid Clustering Algorithm Based on Improved Density Peak Clustering
## 1 Introduction  
Clustering algorithms, as a category of unsupervised learning techniques, are employed to partition objects within a dataset into clusters based on shared characteristics. The primary objective is to increase the similarity among objects within the same cluster while decreasing the similarity between objects in different clusters. This is achieved by maximizing intra-cluster similarity and minimizing inter-cluster similarity. The fundamental concept underlying clustering algorithms is to uncover inherent structures and patterns within the dataset without relying on pre-defined category labels. These algorithms determine whether objects should be grouped into the same cluster by evaluating their similarity or distance from each other. Clustering algorithms find extensive applications across diverse domains. These include data mining, as demonstrated by \"density-based algorithms for discovering clusters in noisy large spatial databases\" [1], image processing, as illustrated in \"efficient clustering methods for color segmentation of spatial images\" [2], and bioinformatics, for tasks such as protein clustering for structural prediction [3]. They are also used in social network analysis, encompassing the identification of critical nodes through graph entropy [4], andmarket analysis, which includes customer segmentation using clustering techniques and social network analysis [5]. Notably, recent work by [PERSON], [PERSON], and [PERSON] in 2017 introduced a method called IDPC (improved density peak clustering) [6], which aimed at enhancing DPC-KNN by employing specific label propagation techniques based on voting strategies and local object density. In a similar vein, their work in 2019 introduced the DPC-DLP method, incorporating the concept of k-nearest neighbors to compute both global cutoff parameters and the local density of each data point. Subsequently, they applied a graph-based label propagation technique to assign labels to the remaining points, ultimately forming the final clusters. Nonetheless, both of these methods can encounter issues related to unstable and fluctuating cluster numbers when selecting density peak points for clustering. To address this limitation, a novel approach known as the hybrid clustering algorithm based on improved density peak clustering has been proposed. This algorithm, combining density peak clustering and mean-shift (DPC-MS), primarily comprises three key steps. First, in the initial stage, the mean-shift algorithm, augmented with kernel functions and adaptive bandwidth, is employed for iterative shifts to identify all local density extremum points. Following this, the second step calculates the adaptive distance from each data point to its nearest local density extremum point, following the principles of the DPC algorithm, thereby assigning the point to the closest local density extremum point. Finally, in the third step, a distance metric is devised. If the distance metric between two local density extremum points falls below a predefined threshold, they are grouped together to form a cluster. This study introduces an improved density peak clustering algorithm that combines DPC (density peak clustering) with mean-shift, named DPC-MS. Through iterative experimentation and enhancements on classic benchmark datasets, the superiority of the DPC-MS algorithm in terms of clustering accuracy and robustness compared to other clustering algorithms is demonstrated. The DPC-MS algorithm demonstrates significant advantages in precision and robustness compared to other clustering algorithms. It not only overcomes the challenges faced by the DPC algorithm in effectively handling manifold data but also addresses the limitations of mean-shift in potentially misclassifying non-local density peak points.