Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1023/A:1008284015704 | Journal of Global Optimization |
Keywords | Field | DocType |
Pattern recognition,non-convex optimization,set separation | Discrete mathematics,Combinatorics,Non convex optimization,Branch and bound,Mathematical optimization,Disjoint sets,Separable space,Regular polygon,Hyperplane,Karush–Kuhn–Tucker conditions,Mathematics | Journal |
Volume | Issue | ISSN |
11 | 4 | 1573-2916 |
Citations | PageRank | References |
7 | 0.89 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James E. Falk | 1 | 297 | 68.47 |
| Emma Lopez-Cardona | 2 | 7 | 0.89 |