Distance metric learning-based multi-granularity neighborhood rough sets

Attribute reduction is a hot research topic in data mining, in which rough set theory-based attribute reduction methods have been widely focused. The neighborhood rough set (NRS) model has good generalization performance and practicality in uncertainty reasoning, so it is often used for attribute reduction in recent years. Calculating the distance between samples in different attribute spaces is a key step in the NRS-based attribute reduction methods, which directly affects the performance of the reduction algorithm. However, the NRS model uses a fixed computational paradigm in calculating the distance between samples and does not consider the influence of labels in the attribute spaces on the distance calculation, which is not conducive to improving the performance of the reduction algorithm. Distance metric learning takes full account of the labels information in the multi-dimensional attribute space, and it can learn the distance between samples by taking into account the integrated principle that samples with the same label are closer and samples with different labels are further away, which helps to reduce the classification uncertainty. Inspired by this, this paper firstly incorporates distance metric learning into the NRS model from the perspective of multi-dimensional attribute space and proposes a distance metric learning-based multi-granularity neighborhood rough set (DmlMNRS) model. The related properties of the DmlMNRS model are also introduced and proved. Then, the DmlMNRS-based attribute reduction criterion and the significance of the attributes are defined. A DmlMNRS-based heuristic attribute reduction (DMNHAR) algorithm is designed based on this. Finally, experiments are performed on fifteen publicly datasets, and the experimental results show that the proposed algorithm has better robustness and classification performance.