An incremental algorithm for attribute reduction with variable precision rough sets

Display Omitted Two Boolean row vectors are introduced to characterize the disdernibility matrix and reduct.Rather than the whole discernibility matrix, minimal elements are incrementally computed.The attribute reduction process is studied to reveal how to add and delete attributes.Our incremental algorithm is developed by the adoption of the attribute reduction process.The experimental results show our method can handle datasets with large samples. Attribute reduction with variable precision rough sets (VPRS) attempts to select the most information-rich attributes from a dataset by incorporating a controlled degree of misclassification into approximations of rough sets. However, the existing attribute reduction algorithms with VPRS have no incremental mechanisms of handling dynamic datasets with increasing samples, so that they are computationally time-consuming for such datasets. Therefore, this paper presents an incremental algorithm for attribute reduction with VPRS, in order to address the time complexity of current algorithms. First, two Boolean row vectors are introduced to characterize the discernibility matrix and reduct in VPRS. Then, an incremental manner is employed to update minimal elements in the discernibility matrix at the arrival of an incremental sample. Based on this, a deep insight into the attribute reduction process is gained to reveal which attributes to be added into and/or deleted from a current reduct, and our incremental algorithm is designed by this adoption of the attribute reduction process. Finally, experimental comparisons validate the effectiveness of our proposed incremental algorithm.