Artículo
Gauge Distances and Median Hyperplanes
Autor/es | Plastria, Frank
Carrizosa Priego, Emilio José |
Departamento | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Fecha de publicación | 2001-01-01 |
Fecha de depósito | 2021-04-23 |
Publicado en |
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Resumen | A median hyperplane in d-dimensional space minimizes the
weighted sum of the distances from a finite set of points to it. When the
distances from these points are measured by possibly different gauges,
we prove the ... A median hyperplane in d-dimensional space minimizes the weighted sum of the distances from a finite set of points to it. When the distances from these points are measured by possibly different gauges, we prove the existence of a median hyperplane passing through at least one of the points. When all the gauges are equal, some median hyperplane will pass through at least dA1 points, this number being increased to d when the gauge is symmetric, i.e. the gauge is a norm. Whereas some of these results have been obtained previously by different methods, we show that they all derive from a simple formula for the distance of a point to a hyperplane as measured by an arbitrary gauge. |
Cita | Plastria, F. y Carrizosa Priego, E.J. (2001). Gauge Distances and Median Hyperplanes. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 110 (1), 173-182. |
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