Local Weighted Neighborhood Rough Sets for Weakly Labeled Data

Local rough set models are efficient rough data analysis methods for weakly labeled data in the rough set field. However, the existing local models do not distinguish the importance of different attributes to decisions when describing and defining binary relations, resulting in inaccurate information granules or classes, which affects the accuracy of concept approximation. In this paper, we choose local neighborhood rough sets as the representative model, and then propose Local Weighted Neighborhood Rough Sets (LWNRS). First, the importance of attributes to decisions is quantified by combining the supervised information of labeled data and the structural information of unlabeled data, and an attribute weighted method based on semi-supervised dynamic optimization is proposed. Meanwhile, the weighted neighborhood relation and neighborhood classes of objects are defined under weakly labeled data, and the WLNRS model is constructed. In addition, the weighted dependency is proposed to measure the data uncertainty, and the relationships among WLNRS and other relevant local and global models are deeply explored. Finally, the efficiency and accuracy of WLNRS in concept approximation are verified by comparison.