Second-order cone programming support vector machine based on generalized memory kernel

This paper proposes a new robust support vector machine framework based on generalized memory kernel and second-order cone programming. Aiming at the generalization limitations and insufficient memory ability (i.e., fitting ability) of traditional SVM in an environment with uncertain data distribution, an innovative linear combination structure of dual-scale radial basis kernel functions is designed: the wide-scale kernel $ K_{g} $(with small bandwidth parameter $ \sigma $) captures global patterns to enhance generalization performance, while the narrow-scale kernel $ K_{g} $ (with large bandwidth parameter $ \sigma_{m}\gg\sigma $) achieves accurate fitting of training samples. The weight coefficient $ \tau $ dynamically adjusts the memory-generalization balance. On this basis, the kernel mapping is embedded into the distributionally robust framework of SOCP-SVM, and the finally constructed optimization problem is efficiently solved in the form of a linear objective function and three sets of second-order cone constraints. Experiments show that this method ensures the upper bound of classification error rate ($ \leq1-\eta_{i} $) and adaptively controls the bias-variance characteristics of the model by adjusting $ \tau $, significantly improving the classification robustness of small-sample and noisy data.