Multi-class SVMs: From Tighter Data-Dependent Generalization Bounds to Novel Algorithms

Part of Advances in Neural Information Processing Systems 28 (NIPS 2015)

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Yunwen Lei, Urun Dogan, Alexander Binder, Marius Kloft


This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially improving the state-of-the-art linear dependence in the existing data-dependent generalization analysis. The theoretical analysis motivates us to introduce a new multi-class classification machine based on lp-norm regularization, where the parameter p controls the complexity of the corresponding bounds. We derive an efficient optimization algorithm based on Fenchel duality theory. Benchmarks on several real-world datasets show that the proposed algorithm can achieve significant accuracy gains over the state of the art.