Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
Mathematical Programming: Series A and B
Minimum distance to the complement of a convex set: duality result
Journal of Optimization Theory and Applications
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Polyhedral Boundary Projection
SIAM Journal on Optimization
Minimum L1-distance projection onto the boundary of a convex set: simple characterization
Journal of Optimization Theory and Applications
The Maximum Box Problem and its Application to Data Analysis
Computational Optimization and Applications
Duality and Geometry in SVM Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Fast and Robust Smallest Enclosing Balls
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
The class cover problem and its applications in pattern recognition
The class cover problem and its applications in pattern recognition
Machine learning with data dependent hypothesis classes
The Journal of Machine Learning Research
Approximation Algorithms for the Class Cover Problem
Annals of Mathematics and Artificial Intelligence
Random Graphs for Statistical Pattern Recognition
Random Graphs for Statistical Pattern Recognition
Efficient Algorithms for the Smallest Enclosing Ball Problem
Computational Optimization and Applications
Spanned patterns for the logical analysis of data
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
A novel SVM Geometric Algorithm based on Reduced Convex Hulls
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
The convex subclass method: combinatorial classifier based on a family of convex sets
MLDM'05 Proceedings of the 4th international conference on Machine Learning and Data Mining in Pattern Recognition
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We propose a general framework for nonparametric classification of multi-dimensional numerical patterns. Given training points for each class, it builds a set cover with convex sets each of which contains some training points of the class but no points of the other classes. Each convex set has thus an associated class label, and classification of a query point is made to the class of the convex set such that the projection of the query point onto its boundary is minimal. In this sense, the convex sets of a class are regarded as ''prototypes'' for that class. We then apply this framework to two special types of convex sets, minimum enclosing balls and convex hulls, giving algorithms for constructing a set cover with them and for computing the projection length onto their boundaries. For convex hulls, we also give a method for implicitly evaluating whether a point is contained in a convex hull, which can avoid computational difficulty for explicit construction of convex hulls in high-dimensional space.