INGB: Informed Nonlinear Granular Ball Oversampling Framework for Noisy Imbalanced Classification

In classification problems, the datasets are usually imbalanced, noisy or complex. Most sampling algorithms only make some improvements to the linear sampling mechanism of the synthetic minority oversampling technique (SMOTE). Nevertheless, linear oversampling has several unavoidable drawbacks. Linear oversampling is susceptible to overfitting, and the synthetic samples lack diversity and rarely account for the original distribution characteristics. An informed nonlinear oversampling framework with the granular ball (INGB) as a new direction of oversampling is proposed in this paper. It uses granular balls to simulate the spatial distribution characteristics of datasets, and informed entropy is utilized to further optimize the granular-ball space. Then, nonlinear oversampling is performed by following high-dimensional sparsity and the isotropic Gaussian distribution. Furthermore, INGB has good compatibility. Not only can it be combined with most SMOTE-based sampling algorithms to improve their performance, but it can also be easily extended to noisy imbalanced multi-classification problems. The mathematical model and theoretical proof of INGB are given in this work. Extensive experiments demonstrate that INGB outperforms the traditional linear sampling frameworks and algorithms in oversampling on complex datasets.