Three-Level Noise-Tolerance Granular-Ball Distinguishing Measures and Feature Subset Selection

Uncertainty modeling with different granularity structures is a research hotspot in granular computing. However, most granularity-related uncertainty measures lack effective means to represent and exploit the inherent granularity information in data, making it difficult for them to capture the distribution characteristics of samples and causing noise samples in high-aggregation regions to be misidentified. Meanwhile, they rarely involve noise-resistance mechanisms and struggle to accurately characterize the differences between samples in strongly disturbed environments, resulting in sensitivity to noise and insufficient robustness. Motivated by these issues, we investigate a novel granular-ball distinguishing measure that enhances noise-resistance on three levels: the algebraic perspective (dependency function), information theory (variable-precision entropy), and granular-ball computing (granulation mechanism). To this end, we define a relative-distance fuzzy similarity relation that fully considers local and global data distribution, thus effectively mitigating the influence of noise and outliers. A relative-distance granular-ball dependency function is then introduced by means of the relative-distance fuzzy similarity relation and fuzzy decision. Moreover, several granular-ball fuzzy entropy measures are presented, incorporating a variable-precision view to flexibly deal with noise and uncertainty. Finally, a granular-ball distinguishing measure is presented to comprehensively evaluate the distinguishing ability of candidate features. From the view of maintaining the classification ability, we further developed a heuristic feature selection algorithm with the distinguishing measure. Numerical experiments on 18 benchmark datasets demonstrate the effectiveness and robustness of the proposed model, as well as its superiority over six state-of-the-art comparative algorithms.