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

Abstract: 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.