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The Methods for Approximation of Principal Points for Binary Distributions on the Basis of Submodularity

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  • Haruka Yamashita
  • Hideo Suzuki

Abstract

Principal points for binary distributions are able to be defined based on Flury’s principal points (1990). However, finding principal points for binary distributions is hard in a straightforward manner. In this article, a method for approximating principal points for binary distributions is proposed by formulating it as an uncapacitated location problem. Moreover, it is shown that the problem of finding principal points can be solved with the aid of submodular functions. It leads to a solution whose value is at least (1 − 1/e) times the optimal value.

Suggested Citation

  • Haruka Yamashita & Hideo Suzuki, 2015. "The Methods for Approximation of Principal Points for Binary Distributions on the Basis of Submodularity," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2291-2309, June.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:11:p:2291-2309
    DOI: 10.1080/03610926.2013.781645
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