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Algorithms for the Spatial Median

In: Modern Nonparametric, Robust and Multivariate Methods

Author

Listed:
  • John T. Kent

    (University of Leeds, Department of Statistics)

  • Fikret Er

    (Anadolu University, Open Education Faculty, Yunusemre Campus)

  • Patrick D. L. Constable

Abstract

The spatial median spatial median can be defined as the unique minimum of a strictly convex objective function. Hence, its computation through an iterative algorithm ought to be straightforward. The simplest algorithm is the steepest descent steepest descent Weiszfeld Weiszfeld algorithm algorithm, as modified by Ostresh Ostresh-Vardi-Zhang algorithm and by Vardi and Zhang Vardi-Zhang algorithm . Another natural algorithm is Newton-Raphson. Newton-Raphson algorithm Unfortunately, all these algorithms can have problems near data points; indeed, Newton-Raphson can converge to a non-optimal data point, even if a line search is included! However, by combining these algorithms, a reliable and efficient “hybrid” hybrid algorithm algorithm can be developed.

Suggested Citation

  • John T. Kent & Fikret Er & Patrick D. L. Constable, 2015. "Algorithms for the Spatial Median," Springer Books, in: Klaus Nordhausen & Sara Taskinen (ed.), Modern Nonparametric, Robust and Multivariate Methods, edition 1, chapter 0, pages 205-224, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22404-6_12
    DOI: 10.1007/978-3-319-22404-6_12
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