Generalized AUC Maximization Core Vector Machine: A Multi-Kernel Learning Approach for Fast Imbalanced Classification

Imbalanced classification remains a fundamental challenge in machine learning, where the Area Under the ROC Curve (AUC) is widely used for threshold-independent ranking evaluation, especially in AUC maximization studies. Existing AUC maximization methods suffer from two critical limitations: they rely on single fixed kernels that fail to capture complex data structures, and they incur prohibitive computational costs due to pairwise constraint construction. To address these issues, we propose the Generalized AUC Maximization Core Vector Machine (GAM-CVM), a fast imbalanced classification framework integrating multi-kernel learning with core vector machine optimization. Multiple affinity graphs are constructed from complementary perspectives and fused via cross-diffusion into a unified kernel matrix that respects the intrinsic data manifold. This fused kernel is embedded into a generalized AUC objective with a flexible ranking margin. Given the fused kernel matrix, the optimization stage of GAM-CVM achieves asymptotic linear time complexity with respect to the number of sample pairs under a fixed approximation accuracy by reformulating the learning objective as a center-constrained minimum enclosing ball problem. Extensive experiments demonstrate that GAM-CVM achieves the best overall average ranking and significantly outperforms most competing methods while maintaining the lowest optimization-stage running time.