Optimal granularity selection based on algorithm stability with application to attribute reduction in rough set theory
Optimal granularity selection based on algorithm stability with application to attribute reduction in rough set theory
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DOI：
10.1016/j.ins.2023.119845
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发表时间：
2024-01
期刊：
影响因子：
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通讯作者：
Yue Gao;Degang Chen;Hui Wang
中科院分区：
文献类型：
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作者：
Yue Gao;Degang Chen;Hui Wang
最优粒度选择是粗糙集的一个关键问题，它可以生成决策规则，为新样本分配相应的决策标签。目前最优粒度的评价标准主要关注预测算法的实验效果，忽略了粒度与算法泛化能力之间的理论关系。本文研究了上述忽略的问题，提出了一种具有理论保证的最优粒度选择框架。在我们的框架中，引入了一种基于粗糙集的预测算法，该算法将全局置信度作为评分函数，其特征是基于粒度的损失函数。在此基础上，引入机器学习中的稳定性理论，研究了粒度与算法泛化能力之间的关系。推导了算法的泛化误差界，为最佳粒度选择提供了理论保证。最后，提出了一种具有理论保证的最优粒度选择策略，该策略结合现有的属性约简方法，设计了通过约简相对不重要的属性来生成最优粒度的属性再约简算法。数值实验验证了最优粒度选择框架的合理性，证明了属性重约算法生成的最优粒度的有效性。
Optimal granularity selection is a key issue in rough set, by which decision rules can be generated to assign corresponding decision labels for new samples. The current evaluation criteria of optimal granularity mainly focus on the experimental effect of prediction algorithms, thus ignoring the theoretical relationship between granularity and the generalization ability of algorithms. In this paper, we study the issue overlooked above and propose a novel framework for optimal granularity selection with theoretical guarantee. In our framework, a rough set-based prediction algorithm that incorporates a global confidence as scoring function is introduced, which is characterized by the granularity-based loss function. On the bias, the relationship between granularity and the generalization ability of algorithm is studied by introducing the stability theory in machine learning. The generalization error bound of algorithm is derived as a theoretical guarantee for optimal granularity selection. Finally, a novel optimal granularity selection strategy with theoretical guarantee is proposed, which is combined with existing attribute reduction methods to design the attribute re-reduction algorithms for generate optimal granularity by reducing the relatively unimportant attributes. Numerical experiments verify the rationality of optimal granularity selection framework and prove the effectiveness of the optimal granularity generated by the attribute re-reduction algorithms.