LGBQPC: Local Granular-Ball Quality Peaks Clustering

The density peaks clustering (DPC) algorithm has attracted considerable attention for its ability to detect arbitrarily shaped clusters based on a simple yet effective assumption. Recent advancements integrating granular-ball (GB) computing with DPC have led to the GB-based DPC (GBDPC) algorithm, which improves computational efficiency. However, GBDPC demonstrates limitations when handling complex clustering tasks, particularly those involving data with complex manifold structures or non-uniform density distributions. To overcome these challenges, this paper proposes the local GB quality peaks clustering (LGBQPC) algorithm, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG). Firstly, an improved GB generation method, termed GB-POJG+, is developed, which systematically refines the original GB-POJG in four key aspects: the objective function, termination criterion for GB division, definition of abnormal GB, and granularity level adaptation strategy. GB-POJG+ simplifies parameter configuration by requiring only a single penalty coefficient and ensures high-quality GB generation while maintaining the number of generated GBs within an acceptable range. In the clustering phase, two key innovations are introduced based on the GB k-nearest neighbor graph: relative GB quality for density estimation and geodesic distance for GB distance metric. These modifications substantially improve the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions. Extensive numerical experiments on 40 benchmark datasets, including both synthetic and publicly available datasets, validate the superior performance of the proposed LGBQPC algorithm.

Generation of Granular-Balls for Clustering Based on the Principle of Justifiable Granularity

Efficient and robust data clustering remains a challenging task in the field of data analysis. Recent efforts have explored the integration of granular-ball (GB) computing with clustering algorithms to address this challenge, yielding promising results. However, existing methods for generating GBs often rely on single indicators to measure GB quality and employ threshold-based or greedy strategies, potentially leading to GBs that do not accurately capture the underlying data distribution. To address these limitations, this article introduces a novel GB generation method. The originality of this method lies in leveraging the principle of justifiable granularity to measure the quality of a GB for clustering tasks. To be precise, we define the coverage and specificity of a GB and introduce a comprehensive measure for assessing GB quality. Utilizing this quality measure, the method incorporates a binary tree pruning-based strategy and an anomaly detection method to determine the best combination of sub-GBs for each GB and identify abnormal GBs, respectively. Compared to previous GB generation methods, the new method maximizes the overall quality of generated GBs while ensuring alignment with the data distribution, thereby enhancing the rationality of the generated GBs. Experimental results obtained from both synthetic and publicly available datasets underscore the effectiveness of the proposed GB generation method, showcasing improvements in clustering accuracy and normalized mutual information.