The methods for approximation of principal points for binary distributions on the basis of submodularity

Haruka Yamashita, Hideo Suzuki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Principal points for binary distributions are able to be defined based on Flurys 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.

Original languageEnglish
Pages (from-to)2291-2309
Number of pages19
JournalCommunications in Statistics - Theory and Methods
Volume44
Issue number11
DOIs
Publication statusPublished - 2015 Jun 3

Fingerprint

Principal Points
Submodularity
Binary
Approximation
Submodular Function
Location Problem

Keywords

  • Clustering
  • Data analysis
  • Multivariate binary distribution
  • Uncapacitated location problem

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

The methods for approximation of principal points for binary distributions on the basis of submodularity. / Yamashita, Haruka; Suzuki, Hideo.

In: Communications in Statistics - Theory and Methods, Vol. 44, No. 11, 03.06.2015, p. 2291-2309.

Research output: Contribution to journalArticle

@article{b05c47ec0ee94a2b832a4c55fbd8c40b,
title = "The methods for approximation of principal points for binary distributions on the basis of submodularity",
abstract = "Principal points for binary distributions are able to be defined based on Flurys 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.",
keywords = "Clustering, Data analysis, Multivariate binary distribution, Uncapacitated location problem",
author = "Haruka Yamashita and Hideo Suzuki",
year = "2015",
month = "6",
day = "3",
doi = "10.1080/03610926.2013.781645",
language = "English",
volume = "44",
pages = "2291--2309",
journal = "Communications in Statistics - Theory and Methods",
issn = "0361-0926",
publisher = "Taylor and Francis Ltd.",
number = "11",

}

TY - JOUR

T1 - The methods for approximation of principal points for binary distributions on the basis of submodularity

AU - Yamashita, Haruka

AU - Suzuki, Hideo

PY - 2015/6/3

Y1 - 2015/6/3

N2 - Principal points for binary distributions are able to be defined based on Flurys 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.

AB - Principal points for binary distributions are able to be defined based on Flurys 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.

KW - Clustering

KW - Data analysis

KW - Multivariate binary distribution

KW - Uncapacitated location problem

UR - http://www.scopus.com/inward/record.url?scp=84933074037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84933074037&partnerID=8YFLogxK

U2 - 10.1080/03610926.2013.781645

DO - 10.1080/03610926.2013.781645

M3 - Article

AN - SCOPUS:84933074037

VL - 44

SP - 2291

EP - 2309

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 11

ER -