A locally distributed rough set model for feature selection and prototype learning

Neighborhood rough set (NRS) theory is a tool for handling data uncertainty based on neighborhood theory and has been successfully applied to feature selection and classification modeling. In practical applications, the data distribution often exhibits significant density variations, posing a challenge to the classical NRS model. To address this issue, this study proposes a locally distributed rough set (DRS) model that can adaptively select the neighborhood radius for each sample and designs data reduction algorithms accordingly. In this work, the concept of distributed neighborhood is introduced, followed by an exploration of a locally distributed rough set model based on distributed neighborhood. This model can dynamically determine the appropriate neighborhood radius for each sample based on local distribution information. Additionally, certain properties of the DRS model are summarized and proven. Subsequently, feature selection and sample reduction algorithms are developed based on the DRS model. Experimental results demonstrate the effectiveness and efficiency of these proposed algorithms, indicating that the designed DRS model is both feasible and generalizable.