AFNFS: Adaptive fuzzy neighborhood-based feature selection with adaptive synthetic over-sampling for imbalanced data

• The closeness is defined according to the variance distance between samples from the minority classes. This pair set of neighboring samples in the minority classes is further given, and synthetic samples based on the random interpolation are expressed. Thus, an improved adaptive synthetic over-sampling model is constructed to obtain this balanced decision system consisting of those synthetic and original samples. • An adaptive fuzzy neighborhood radius is defined according to the data margins of all homogeneous and heterogeneous samples, and the similarity relationship based on the adaptive fuzzy neighborhood radius and its similarity matrix is proposed. The adaptive fuzzy neighborhood granule, adaptive fuzzy membership degree, and upper and lower approximations are constructed to design a new FNRS model. • By combining the roughness of the evaluation boundary region with the adaptive fuzzy neighborhood entropy, adaptive fuzzy neighborhood joint entropy with roughness in fuzzy neighborhood decision systems is constructed for evaluating the uncertainty. A heuristic adaptive fuzzy neighborhood-based feature selection algorithm with the tolerance parameter is proposed for imbalanced data classification. The classification efficiency of majority classes for imbalanced data is so concerned in real-world applications. Almost fuzzy neighborhood radius still needs to be manually set and many entropy measures may ignore the boundary region of data, these limitations will result in the poor classification effect. To address these limitations, this paper designs a novel adaptive fuzzy neighborhood-based feature selection method for imbalanced data with adaptive synthetic over-sampling. First, the closeness is defined according to the variance distance between the samples of the minority class, the pair set of neighboring samples is designed, and then an improved adaptive synthetic over-sampling model is presented for constructing balanced decision systems consisting of the synthetic samples and original samples. Second, an adaptive fuzzy neighborhood radius is developed when using the data margins of all homogeneous and heterogeneous samples. Then the adaptive fuzzy neighborhood granule and upper and lower approximations are defined to construct a new FNRS model. Thus, approximate accuracy and roughness are presented to measure the uncertainty from the fuzzy and rough perspectives for imbalanced data. Third, by combining the roughness with adaptive fuzzy neighborhood entropy, adaptive fuzzy neighborhood joint entropy is constructed to evaluate the uncertainty in fuzzy neighborhood decision systems from two viewpoints of algebra and information. Then the reduced set and the significance of the feature are further developed. Finally, this improved adaptive synthetic over-sampling algorithm is designed to aim to build this balanced decision system, and an adaptive fuzzy neighborhood-based feature selection algorithm with the tolerance parameter is developed to achieve an optimal feature subset. Experiments on 26 imbalanced datasets demonstrate that the constructed algorithms compared to the other related algorithms are effective.