A robust clustering algorithm based on weighted optimization of fuzzy feature difference using shadow sets

Robustness is a critical metric for evaluating the performance of clustering algorithms, particularly their stability and reliability across various datasets. Despite the significant challenges posed by noise and outliers, robust clustering methods have shown resilience in uncovering inherent data structures. This study expands on foundational work from the turn of the century, advancing robust clustering through strategic innovation. We introduce a novel algorithm—robust clustering algorithm based on weighted optimization of fuzzy feature difference using shadow sets (RWFS). The algorithm implements multi-granular data partitioning based on granular computing to enhance clustering adaptability; it optimizes the handling of boundary samples using shadow set theory, thereby strengthening the identification of fuzzy regions; and it evaluates the purity within clusters through information entropy to optimize the clustering structure. The integration of these three aspects significantly enhances the algorithm's robustness and clustering accuracy in the presence of complex data and noise. Using the modified silhouette coefficient (MSC) as an internal metric, our evaluations confirm RWFS's ability to reveal underlying patterns in datasets affected by various noise types. Under 10% outlier noise, the average MSC values across all benchmark datasets are 0.2275. Under 5% inter cluster noise, the average value of MSC is 0.6037. Under 10% Global Gaussian noise, the average value of MSC is 0.4686. The maximum ACC of robust experiment is 0.8436. This approach enhances robustness and facilitates more nuanced characterization of relationships within clustering algorithms. Our findings highlight RWFS's potential as a powerful tool in machine learning, with broad implications for applications where data integrity and interpretability are crucial. The code is publicly available online at https://github.com/yu7bin/RWFS.