Fuzzy-Rough Bireducts With Supervised Multiscale Granulation

The inherent characteristics involved in data can be mined from multi-scale information systems by extracting information from different value levels of features. In real applications, noise data and irrelevant or redundant features affect the generality of learning models. Therefore, keeping meaningful features and avoiding the effect of noise is essential for feature selection in a multi-scale information system. In bireduct, multi-scale granulation can be used to characterize the importance and correlation of features at different scales. However, little work has taken the distribution of multi-scale data into account when granulating it. In addition, these approaches focus on solving the task of multi-scale data reduction only from the dimension perspective. To this end, a fuzzy-rough bireduct with supervised multi-scale granulation (FrBSmg) is proposed. First, the supervised multi-scale fuzzy granulation based on data distribution is constructed. Then, scaled uncertainty measures are defined to describe the fuzzy relevance of each feature. Furthermore, the global and local distributions of a sample are characterized simultaneously based on the positive region, which can reflect the degree of a sample belonging to some class, and the supervised fuzzy similarity relation can describe the degree of a sample belonging to its class. A strategy of Feature-Correlated Selection and Sample-Noisy Removal is devised for bireduct. Finally, the experimental results on twenty-one public datasets show the effectiveness of FrBSmg.