用球形粒度代替点,让模糊粗糙集更抗噪、更高效。
GBFRS: Robust Fuzzy Rough Sets via Granular-ball Computing
- 用不同大小的球形粒度覆盖样本空间,替代传统点式表示。
- 在多个数据集上显著提升特征选择准确率,优于基线方法。
- 适合高维大数据中的鲁棒特征提取,尤其抗噪声能力强。
模糊粗糙集理论在处理复杂属性数据方面表现优异,具备坚实的数学基础,并与机器学习中的核方法紧密关联。基于该理论的属性约简算法和分类器在高维多变量复杂数据中展现出良好性能。然而,大多数现有模型在最细粒度下运行,效率低且对噪声敏感,尤其在高维大数据场景下。因此,提升模糊粗糙集模型的鲁棒性对有效特征选择至关重要。多粒度球形粒度计算是近期发展,通过不同大小的球形粒度自适应表示和覆盖样本空间,基于这些粒度进行学习。本文提出将多粒度球形粒度计算融入模糊粗糙集理论,用球形粒度替代样本点。球形粒度的粗粒度特性使模型更具鲁棒性。此外,提出一种新球形粒度生成方法,可扩展至基于球形粒度计算的整个监督学习框架。采用前向搜索算法,通过依赖函数定义特征与类别间的相关性,选择特征序列。实验表明,所提模型在有效性与优越性上均优于基线方法。
原文摘要 · Abstract (English)
Fuzzy rough set theory is effective for processing datasets with complex attributes, supported by a solid mathematical foundation and closely linked to kernel methods in machine learning. Attribute reduction algorithms and classifiers based on fuzzy rough set theory exhibit promising performance in the analysis of high-dimensional multivariate complex data. However, most existing models operate at the finest granularity, rendering them inefficient and sensitive to noise, especially for high-dimensional big data. Thus, enhancing the robustness of fuzzy rough set models is crucial for effective feature selection. Muiti-garanularty granular-ball computing, a recent development, uses granular-balls of different sizes to adaptively represent and cover the sample space, performing learning based on these granular-balls. This paper proposes integrating multi-granularity granular-ball computing into fuzzy rough set theory, using granular-balls to replace sample points. The coarse-grained characteristics of granular-balls make the model more robust. Additionally, we propose a new method for generating granular-balls, scalable to the entire supervised method based on granular-ball computing. A forward search algorithm is used to select feature sequences by defining the correlation between features and categories through dependence functions. Experiments demonstrate the proposed model's effectiveness and superiority over baseline methods.
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