Computational geometry: an introduction
Computational geometry: an introduction
Discriminant analysis via mathematical programming: certain problems and their causes
Computers and Operations Research
A new implicit enumeration scheme for the discriminant analysis problem
Computers and Operations Research
Pattern classification by concurrently determined piecewise linear and convex discriminant functions
Computers and Industrial Engineering - Special issue: Computational intelligence and information technology applications to industrial engineering selected papers from the 33 rd ICC&IE
A Heuristic Method for Selecting Support Features from Large Datasets
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Pattern classification by concurrently determined piecewise linear and convex discriminant functions
Computers and Industrial Engineering
Separation of data via concurrently determined discriminant functions
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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Given a pair of finite disjoint setsA andB inR^n, a fundamental problem with many important applications isto efficiently determine a hyperplaneH(w,λ) whichseparates these sets when they are separable, or ’nearly‘ separates themwhen they are not. We seek a hyperplane which minimizes a natural errormeasure in the latter case, and so will ’surgically‘ separate the sets. Whenthe sets are separable in a strong sense, we show that the problem is aconvex program with a unique solution, which has been investigated byothers. Using the KKT conditions, we improve on an existing algorithm. Whenthe sets are not separable, the problem is nonconvex, generally with properlocal solutions, and we solve an equivalent problem by Branch and Bound.Numerical results are presented.