Instance selection and attribute reduction based on the nearest tolerance relation

To address the problem of data classification uncertainty caused by redundant information in information systems (IIS), a tolerance relation is used to expand rough sets, and an instance selection algorithm (ISM) and attribute reduction algorithm (ARM) based on the nearest tolerance relation are proposed. Firstly, the process of computing the approximate set is vectorized using a matrix approach. Based on the results of the lower approximations, an instance selection algorithm (ISM) is designed to determine the instance set. An attribute reduction algorithm (ARM) is designed using attribute dependency as heuristic information. Starting from a core set of attributes in a bottom-up manner, non-core attributes are added to the core set based on the importance of external attributes, resulting in a core reduction set. The experimental results on nine UCI datasets show that the matrix based on ISM algorithm and ARM algorithm effectively remove redundant samples and attributes, and improve various performance indicators. Compared with the original dataset, the ISM algorithm achieved an average instance reduction ratio of 44.2%, and the ARM algorithm achieved an average attribute reduction ratio of 33%. Compared with other attribute reduction algorithms, the ARM algorithm has an overall improvement of 1.15% in classification accuracy on KNN and SVM classifiers.