Gravitational least squares twin support vector machine based on optimal angle for class imbalance learning

This paper introduces the Gravitational Least Squares Twin Support Vector Machine for Class Imbalance Learning (GLSTSVM-CIL), a novel binary classification method designed to address critical limitations in existing approaches for imbalanced large-scale datasets. Traditional methods like Fuzzy TSVM and KNN-based weighting fail to simultaneously capture both global positional relationships and local density characteristics of data points. Our proposed gravitational weighting function innovatively models data samples as masses influenced by their distance from class centroids and neighborhood density, effectively prioritizing representative points while suppressing outliers. The optimization framework uniquely incorporates angular constraints between hyperplanes to enhance structural risk control and generalization capability. For scalability, we reformulate the solution into a linear system solvable via conjugate gradient methods, avoiding computationally expensive matrix inversions. Comprehensive evaluations on 92 datasets (including synthetic, noisy, medical, text, and large-scale NDC benchmarks) demonstrate GLSTSVM-CIL’s superior performance, particularly in minority-class recognition where it achieves average F1-Score improvements over baseline methods. The model maintains robust Accuracy under high noise (20 %) and extreme class imbalance (ratio 20:1) while ables to process datasets up to 50,000 samples.