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Geometric Median

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Encyclopedia of GIS

  • 271 Accesses

FormalPara Synonyms

Bivariate median; Euclidean median; Generalized Fermat point; L1 median; Median center; Minimum aggregate travel pointSpatial median; Weber problem

Definition

Given a set of points in Euclidean space, geometric median is a point which represents the central tendency of the set. The geometric median of points is selected in such a way that it minimizes the sum of distances from itself to the other points in the set. Geometric median is an important concept in statistics where the central tendency of the set is required regardless of the outliers present. It is also used for the facility location problems which aim to minimize the cost of transportation. It is equivariant under Euclidean similarity transformations, and it is unique under the condition that the points are not collinear, and the number of points in the set is odd (Haldane 1948). Finding the geometric median is a challenging task since no polynomial time algorithm is known, and the solutions for the...

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References

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Author information

Authors and Affiliations

  1. Computer Science and Engineering, University of Minnesota, 55455, Minneapolis, MN, USA

    Emre Eftelioglu

Authors
  1. Emre Eftelioglu
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Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

  2. Management Science and Information Systems Department, Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ, USA

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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Eftelioglu, E. (2017). Geometric Median. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_1555

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