Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
Mathematical Programming: Series A and B
The nature of statistical learning theory
The nature of statistical learning theory
Computer Vision and Image Understanding
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
Polyhedral Boundary Projection
SIAM Journal on Optimization
Training Invariant Support Vector Machines
Machine Learning
SVMTorch: support vector machines for large-scale regression problems
The Journal of Machine Learning Research
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Algorithms for the Computation of Reduced Convex Hulls
AI '09 Proceedings of the 22nd Australasian Joint Conference on Advances in Artificial Intelligence
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We propose an algorithm to approximate each class region by a small number of approximated convex hulls and to use these for classification. The classifier is one of non-kernel maximum margin classifiers. It keeps the maximum margin in the original feature space, unlike support vector machines with a kernel. The construction of an exact convex hull requires an exponential time in dimension, so we find an approximate convex hull (a polyhedron) instead, which is constructed in linear time in dimension. We also propose a model selection procedure to control the number of faces of convex hulls for avoiding over-fitting, in which a fast procedure is adopted to calculate an upper-bound of the leave-one-out error. In comparison with support vector machines, the proposed approach is shown to be comparable in performance but more natural in the extension to multi-class problems.