Attribute reduction is one of the most important research issues in the rough set theory. The purpose of attribute reduction is to find a minimal attribute subset that satisfies some specific criteria, while the minimal attribute subset is called attribute reduct. In this paper, we define a similarity-based attribute reduct based on a clustering perspective. Each decision class is treated as a cluster, and the defined similarity-based attribute reduct can maintain or increase the discriminating ability of different clusters in the case of removing redundant attributes. In view of this, firstly, we define the intra-class similarity for objects in the same decision class and the inter-class similarity for objects between different decision classes. Secondly, we define a similarity-based attribute reduct by maximizing intra-class similarity and minimizing inter-class similarity in the rough set model. Thirdly, by considering the heuristic search strategy, we also design a corresponding reduction method for the proposed attribute reduct. The experimental results indicate that compared with other representative attribute reducts, our proposed attribute reduct can significantly improve the classification performance.

中文翻译：

---

粗糙集理论中基于相似度的属性约简：一种聚类的观点

属性约简是粗糙集理论中最重要的研究问题之一。属性约简的目的是找到满足某些特定条件的最小属性子集，而最小属性子集称为属性归约。在本文中，我们基于聚类的角度定义了基于相似度的属性约简。每个决策类都被视为一个群集，并且在删除冗余属性的情况下，定义的基于相似度的属性归约可以维持或提高不同群集的区分能力。有鉴于此，首先，我们为同一决策类中的对象定义类内相似性，并为不同决策类之间的对象定义类间相似性。其次，我们通过在粗糙集模型中最大化类内相似度和最小化类间相似度来定义基于相似度的属性归约。第三，通过考虑启发式搜索策略，我们还为提出的属性约简设计了相应的约简方法。实验结果表明，与其他代表性属性约简相比，我们提出的属性约简可以显着提高分类性能。