Multicategory discrimination via linear programming
作者:
Kristin P. Bennett,
O.L. Mangasarian,
期刊:
Optimization Methods and Software
(Taylor Available online 1994)
卷期:
Volume 3,
issue 1-3
页码: 27-39
ISSN:1055-6788
年代: 1994
DOI:10.1080/10556789408805554
出版商: Gordon and Breach Science Publishers
关键词: Multicategory discrimination;Machine learning;Linear programming
数据来源: Taylor
摘要:
A single linear program is proposed for discriminating between the elements of κ disjoint point sets in then-dimensional real spaceRn. When the conical hulls of the κ sets are (κ−1)-point disjoint inRn+1, a κ-piece piecewise-linear surface generated by the linear program completely separates the κ sets. This improves on a previous linear programming approach which required that each set be linearly separable from the remaining κ−1 sets. When the conical hulls of the κ sets are not (κ;−1)-point disjoint, the proposed linear program generates an error-minimizing piecewise-linear separator for the κ Sets. For this case it is shown that the null solution is never a unique solver of the linear program and occurs only under the rather rare condition when the mean of each point set equals the mean of the means of the other κ−l sets. This makes the proposed linear computational programming formulation useful for approximately discriminating between κ sets that are not piecewise-linear separable. Computational results are reported for three previously available databases.
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