Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29676
Title: Exact L 2-norm plane separation
Authors: Audet, C
Hansen, P
Karam, A
Ng, CT 
Perron, S
Keywords: L2-norm separation
Linear discrimination
Quadratic programming
Separating plane
Issue Date: 2008
Publisher: Springer Heidelberg
Source: Optimization letters, 2008, v. 2, no. 4, p. 483-495 How to cite?
Journal: Optimization Letters 
Abstract: We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of L p -norm distances to the plane of points lying on the wrong side of it. Despite recent progress, practical techniques for the exact solution of cases other than the L 1 and L ∞-norm were unavailable. We propose and implement a new approach, based on non-convex quadratic programming, for the exact solution of the L 2-norm case. We solve in reasonable computing times artificial problems of up to 20000 points (in 6 dimensions) and 13 dimensions (with 2000 points). We also observe that, for difficult real-life instances from the UCI Repository, computation times are substantially reduced by incorporating heuristic results in the exact solution process. Finally, we compare the classification performance of the planes obtained for the L 1, L 2 and L ∞ formulations. It appears that, despite the fact that L 2 formulation is computationally more expensive, it does not give significantly better results than the L 1 and L ∞ formulations.
URI: http://hdl.handle.net/10397/29676
DOI: 10.1007/s11590-007-0074-1
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