Neighborhoods form a set-level approximation of data distribution for learning tasks. Due to the advantages of data generalization and nonparametric property, neighborhood models have been widely used for data classification. However, the existing neighborhood-based classification methods rigidly assign a certain class label to each data instance and lack the strategies to handle the uncertain instances. The far-fetched certain classification of uncertain instances may suffer serious risks. To tackle this problem, in this article, we propose a novel shadowed set to construct shadowed neighborhoods for uncertain data classification. For the fuzzy-rough transformation in the proposed shadowed set, a step function is utilized to map fuzzy neighborhood memberships to the set of triple typical values {0, 1, 0.5} and thereby partition a neighborhood into certain regions and uncertain boundary (neighborhood shadow). The threshold parameter in the step function for constructing shadowed neighborhoods is optimized through minimizing the membership loss in the mapping of shadowed sets. Based on the constructed shadowed neighborhoods, we implement a three-way classification algorithm to distinguish data instances into certain classes and uncertain case. Experiments validate the proposed three-way classification method with shadowed neighborhoods is effective in handling uncertain data and reducing the classification risk.

中文翻译：

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基于模糊粗糙变换的三向分类阴影邻域


邻域形成学习任务的数据分布的集合级近似。由于数据泛化和非参数性质的优点，邻域模型已被广泛用于数据分类。然而，现有的基于邻域的分类方法严格地为每个数据实例分配特定的类标签，并且缺乏处理不确定实例的策略。对不确定实例的牵强分类可能会带来严重风险。为了解决这个问题，在本文中，我们提出了一种新颖的阴影集来构建阴影邻域以进行不确定的数据分类。对于所提出的阴影集中的模糊粗略变换，利用阶跃函数将模糊邻域隶属度映射到三重典型值{0,1,0.5}的集合，从而将邻域划分为某些区域和不确定边界（邻域阴影） ）。通过最小化阴影集映射中的隶属度损失来优化用于构造阴影邻域的阶跃函数中的阈值参数。基于构建的阴影邻域，我们实现了一种三向分类算法，将数据实例区分为特定类别和不确定情况。实验验证了所提出的阴影邻域三向分类方法能够有效处理不确定数据并降低分类风险。