Gauge Distances and Median Hyperplanes

F. Plastria and E. Carrizosa
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F. Plastria: Vrije Universiteit
E. Carrizosa: Universidad de Sevilla

Journal of Optimization Theory and Applications, 2001, vol. 110, issue 1, No 9, 173-182

Abstract: Abstract 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 d-1 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.

Keywords: gauges; distance to a hyperplane; hyperplane fitting (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (12)

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DOI: 10.1023/A:1017551731021

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