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 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.

Keywords:

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

Mathematics Subject Classification:

• Primary 62H30; Secondary 62-07