Article
Linear separation and approximation by minimizing the sum of concave functions of distances
Author/s | Plastria, Frank
Carrizosa Priego, Emilio José ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Publication Date | 2014-03-01 |
Deposit Date | 2021-04-26 |
Published in |
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Abstract | One recently proposed criterion to separate two data sets in Classification is to use a hyperplane that minimizes the sum of distances to it from all the misclassified data points, where misclassification means lying on ... One recently proposed criterion to separate two data sets in Classification is to use a hyperplane that minimizes the sum of distances to it from all the misclassified data points, where misclassification means lying on the wrong side of the hyperplane, or rather in the wrong halfspace. In this paper we study an extension of this problem: we seek the hyperplane minimizing the sum of concave nondecreasing functions of the distances of misclassified points to it. It is shown that an optimal hyperplane exists containing at least d affinely independent points. This extends the result known for the minimization of the sum of distances, and enables to use combinatorial local-search heuristics for this problem. As a corollary, the same result is obtained for the approximation problem in which a hyperplane minimizing the sum of concave nondecreasing functions of the distances from a set of data points is sought. |
Citation | Plastria, F. y Carrizosa Priego, E.J. (2014). Linear separation and approximation by minimizing the sum of concave functions of distances. 4OR: A Quarterly Journal of Operations Research, 12 (1), 77-85. |
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