# 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 language English 2291-2309 19 Communications in Statistics - Theory and Methods 44 11 https://doi.org/10.1080/03610926.2013.781645 Published - 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

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