Three-Way Outlier Detection Based on Shadowed Granular-Balls

Most existing outlier detection methods rely on a single and fine-grained data representation, making them vulnerable to noise and inefficient in capturing local anomalies. Granular-ball computing (GBC), as an emerging multi-granularity representation and computation framework, provides an effective means to address these issues. Meanwhile, shadow set theory offers a flexible mechanism using three-way decision to handle uncertainty and boundary fuzziness in data. The integration of GBC with shadow set theory combines the strengths of both frameworks, offering promising potential for outlier detection tasks. In this study, we propose a novel outlier detection based on shadowed granular-balls. Firstly, we propose an unsupervised granular-ball generation method with the principle of justifiable granularity. Then, we further present an outlier detection method, named three-way outlier detection based on shadowed granular-ball (3W-SGBD). 3W-SGBD introduces an unsupervised granular-ball generation strategy guided by local density clustering, and adaptively splits granular-balls through a dual-entropy-driven mechanism to better capture local anomalies. In addition, by partitioning each granular-ball into positive, negative, and boundary regions via shadow mapping, 3W-SGBD refines boundary areas to enhance detection accuracy. Finally, extensive comparative experiments are conducted with several state-of-the-art baseline methods on 16 public benchmark datasets. The results show that the effectiveness, efficiency, and robustness of the method proposed in this paper. The code is publicly available at https://github.com/2257352568/3W-SGBD.