Rapid attribute and scale selection with adaptive three-way sampling and neighborhood rough set

As a key issue in knowledge reduction for multi-scale data, attribute and scale selection has attracted increasing attention in recent years. However, with the rapid growth of data volumes, most existing methods are inefficient for large-scale multi-scale data and struggle to effectively handle heterogeneous multi-scale data, significantly limiting their practical applications. To address this situation, this paper proposes a rapid attribute and scale selection method to deal with large nominal-and-numerical mixed multi-scale decision systems (NN-MDSs). First, the theory and algorithm of adaptive incremental support vector data description (AISVDD) are presented. The AISVDD algorithm overcomes the limitations of traditional support vector data description methods and efficiently processes both class-balanced and class-imbalanced data. By using the algorithm, support vectors can be quickly obtained from large data. Next, an adaptive three-way sampling technique is derived by combining AISVDD and three-way decision. With this technique, support vectors are extracted as sampling results and put into the boundary region, and outliers are seen as noise and put into the negative region. This significantly reduces the data size and improves the data quality. Then, a neighborhood rough set model is built to describe NN-MDSs. Multiple concepts and properties are discussed in the model. Finally, a heuristic attribute and scale selection algorithm is designed to simultaneously choose attributes and scales from the sampled NN-MDS. Detailed experiments demonstrate the effectiveness and superiority of the proposed method. The method performs better than state-of-the-art attribute and scale selection methods on both computational efficiency and classification performance under six benchmark classifiers. It is powerful in handling large NN-MDSs with complex characteristics. This work provides new insights into the complex multi-scale data processing.