Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Duality and Geometry in SVM Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Approximating extent measures of points
Journal of the ACM (JACM)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
A novel SVM Geometric Algorithm based on Reduced Convex Hulls
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Simpler core vector machines with enclosing balls
Proceedings of the 24th international conference on Machine learning
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Computational Geometry: Theory and Applications
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Optimization Methods & Software
Maximum margin coresets for active and noise tolerant learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
A new perspective on an old perceptron algorithm
COLT'05 Proceedings of the 18th annual conference on Learning Theory
A fast iterative nearest point algorithm for support vector machine classifier design
IEEE Transactions on Neural Networks
A geometric approach to Support Vector Machine (SVM) classification
IEEE Transactions on Neural Networks
Generalized Core Vector Machines
IEEE Transactions on Neural Networks
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
ACM Transactions on Algorithms (TALG)
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and theory of computation handbook
Approximating parameterized convex optimization problems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
INFORMS Journal on Computing
New approximation algorithms for minimum enclosing convex shapes
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximating parameterized convex optimization problems
ACM Transactions on Algorithms (TALG)
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Following recent work of Clarkson, we translate the coreset framework to the problems of finding the point closest to the origin inside a polytope, finding the shortest distance between two polytopes, Perceptrons, and soft- as well as hard-margin Support Vector Machines (SVM). We prove asymptotically matching upper and lower bounds on the size of coresets, stating that µ-coresets of size (1+o(1)) E*/µ do always exist as µ-0, and that this is best possible. The crucial quantity E* is what we call the excentricity of a polytope, or a pair of polytopes. Additionally, we prove linear convergence speed of Gilbert's algorithm, one of the earliest known approximation algorithms for polytope distance, and generalize both the algorithm and the proof to the two polytope case. Interestingly, our coreset bounds also imply that we can for the first time prove matching upper and lower bounds for the sparsity of Perceptron and SVM solutions.