aSMO: An SMO-Style Solver With Linear Per-Iteration Updates for Large-Scale SVM+ Training

Le résumé fourni par la source

Support Vector Machines with Privileged Information (SVM+) leverage auxiliary data available only during training to improve generalization performance. However, their practical adoption remains limited due to the high computational cost of solving the associated quadratic programming (QP) problem, which scales poorly with dataset size. In this work, we propose Adaptive Sequential Minimal Optimization (aSMO), a specialized SMO-style solver designed for efficient optimization of the SVM+ dual formulation. Unlike classical SMO methods, aSMO operates on irreducible sets of two or three variables to satisfy the coupled equality and inequality constraints inherent to SVM+. The method incorporates a two-phase working set selection strategy and incremental gradient updates, enabling a per-iteration computational complexity that scales linearly with the number of training samples under precomputed kernel matrices. The proposed approach is evaluated on benchmark datasets from computer vision (MNIST) and vibration-based fault diagnosis (CWRU). Experimental results demonstrate that aSMO achieves substantial reductions in training time compared to a standard QP reference baseline, while reaching comparable dual objective values and producing similar test accuracy under identical hyperparameter settings. Furthermore, the method scales effectively to datasets with tens of thousands of samples, where conventional interior-point methods become computationally intractable. These results indicate that aSMO provides a practical and scalable alternative for training SVM+ models, facilitating the practical use of privileged information in large-scale learning scenarios.

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