## 1 Introduction  
In the age of information, there has been an exponential surge in the volume of data, driving the need to extract valuable information and models, which has emerged as a central focus in current research [1]. Accompanying the swift advancements in machine learning, the application of data mining and data publishing [2] assumes paramount significance across diverse industries. Clustering analysis serves as a fundamental aspect of data mining and finds relevance in numerous real-life scenarios [3, 4]. The traditional clustering algorithms can be roughly divided into partition-based algorithms, hierarchy-based algorithms, density-based algorithms, grid-based algorithms, and model-based algorithms [5]. Currently, many scholars have conducted extensive research on clustering algorithms and continuously improved them to enhance their performance. [PERSON] et al. [6] proposed a method combining Kalman filter and K-means for improving the performance of Bayesian classification. This method was able to reduce the computational time for data clustering. [PERSON] et al. [7] proposed a novel CVI (Clustering Validity Index) for fuzzy clustering, i.e., tri-centered relation (TCR) index for noisy datasets. This index solved the difficulty of generating the correct number of clusters when the clustering centers are close to each other and possesses a simple separation processing mechanism. In order to improve the clustering quality of the K-means algorithm, [PERSON] et al. [8] applied the computational geometry method to initialize the clustering center, and proposed an Empty-Circles-based K-means (ECKM) Clustering algorithm. In order to improve the certainty and clarity of information security detection, [PERSON] [9] proposed a DBSCAN clustering algorithm based on big data. This algorithm was a method of applying a big data clustering algorithm to information security detection. In the era of data sharing, it becomes imperative to address the issue of privacy disclosure when dealing with vast amounts of data. Differential privacy technology [10], in comparison to other privacy protection techniques, offers a stringent mathematical definition and a rigorous proof process while providing a quantifiable degree of privacy protection. In recent years, there has been a notable focus on differential privacy-based clustering algorithms, particularly on K-means and its derivative algorithms [11; 12; 13; 14]. However, these algorithms have certain limitations that restrict their applicability to arbitrary types of datasets. These limitations include the need for predetermining the number of clustering centers and multiple iterations to reduce the sensitivity of the initial clustering center. In contrast, the combination of density-based clustering algorithms with differential privacy techniques offers a more versatile and noise-resistant approach. These algorithms do not require multiple iterations and can effectively handle various types of datasets, thereby demonstrating promising potential for practical applications. One noteworthy algorithm in this domain is the DP-DBSCAN algorithm proposed by [PERSON] et al. [15]. This algorithm not only ensures clustering effectiveness but also achieves the desired level of differential privacy protection. Moreover, it is applicable to datasets of varying sizes and dimensions. Another proposed approach by [PERSON] et al. [16] is the differential privacy protection multi-core DBSCAN clustering mode designed specifically for network user data. This approach effectively addresses privacy leakage issues encountered in the data mining process. However, it is worth noting that these algorithms have sensitive parameters and require complex parameter adjustments, which can pose challenges in obtaining stable clustering results. A balancing solution between privacy and availability is offered by the DP-OPTICS algorithm proposed by [PERSON] et al. [17]. However, a key requirement for this algorithm is the need to assume query probabilities in advance and establish an appropriate privacy budget.