  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.
