A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Unconstrained optimization reformulations of variational inequality problems
Journal of Optimization Theory and Applications
Equivalence of variational inequality problems to unconstrained minimization
Mathematical Programming: Series A and B
Pairwise classification and support vector machines
Advances in kernel methods
Combining support vector and mathematical programming methods for classification
Advances in kernel methods
Classification by pairwise coupling
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Reducing multiclass to binary: a unifying approach for margin classifiers
The Journal of Machine Learning Research
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Solving multiclass learning problems via error-correcting output codes
Journal of Artificial Intelligence Research
Operations Research Letters
Spike-timing error backpropagation in theta neuron networks
Neural Computation
Smoothing Newton Method for L1 Soft Margin Data Classification Problem
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Information Sciences: an International Journal
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Multi-class classification is an important and on-going research subject in machine learning. Recently, the ν-K-SVCR method was proposed by the authors for multi-class classification. As many optimization problems have to be solved in multi-class classification, it is extremely important to develop an algorithm that can solve those optimization problems efficiently. In this article, the optimization problem in the ν-K-SVCR method is reformulated as an affine box constrained variational inequality problem with a positive semi-definite matrix, and a regularized version of the nonsmooth Newton method that uses the D-gap function as a merit function is applied to solve the resulting problems. The proposed algorithm fully exploits the typical feature of the ν-K-SVCR method, which enables us to reduce the size of Newton equations significantly. This indicates that the algorithm can be implemented efficiently in practice. The preliminary numerical experiments on benchmark data sets show that the proposed method is considerably faster than the standard Matlab routine used in the original ν-K-SVCR method.