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

Efficient and robust data clustering remains a challenging task in 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 leverages the principle of justifiable granularity (POJG) to measure the quality of a GB for clustering tasks and introduces a novel GB generation method, termed GB-POJG. Specifically, a comprehensive metric integrating the coverage and specificity of a GB is introduced to assess GB quality. Utilizing this quality metric, GB-POJG incorporates a strategy of maximizing overall quality and an anomaly detection method to determine the generated GBs and identify abnormal GBs, respectively. Compared to previous GB generation methods, GB-POJG 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 GB-POJG, showcasing improvements in clustering accuracy and normalized mutual information. All codes have been released at https://zenodo.org/records/13643332.