Shadowed Neighborhoods Based on Fuzzy Rough Transformation for Three-Way Classification

Abstract

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 $\lbrace 0, 1, 0.5\rbrace$ 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.