Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
A New Convex Hull Algorithm for Planar Sets
ACM Transactions on Mathematical Software (TOMS)
Duality and Geometry in SVM Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Optimization over Zonotopes and Training Support Vector Machines
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
A novel SVM Geometric Algorithm based on Reduced Convex Hulls
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
A geometric approach to Support Vector Machine (SVM) classification
IEEE Transactions on Neural Networks
Construction of convex hull classifiers in high dimensions
Pattern Recognition Letters
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Geometric interpretations of Support Vector Machines (SVMs) have introduced the concept of a reduced convex hull. A reduced convex hull is the set of all convex combinations of a set of points where the weight any single point can be assigned is bounded from above by a constant. This paper decouples reduced convex hulls from their origins in SVMs and allows them to be constructed independently. Two algorithms for the computation of reduced convex hulls are presented --- a simple recursive algorithm for points in the plane and an algorithm for points in an arbitrary dimensional space. Upper bounds on the number of vertices and facets in a reduced convex hull are used to analyze the worst-case complexity of the algorithms.