Abstract
In statistics,there are many studies on principal points.The concept of principal points which is proposed by Flury allows us to carry out such an analysis in a variety of applications and also properties of principal points have been studied. Although principal points of a multivariate distribution have widely studied,there is no discussion of principal points for a multivariate binary distribution.
Yamashita and Suzuki have define the principal points for a multivariate binary distribution. Since principal points for a multivariate binary distribution are selected from multivariate binary region,there is a problem of the amount of calculation,since this problem is an NP-hard problem. Yamashita and Suzuki have shown the submodularity of principal points for a multivariate binary distribution and proposed an approximation method based on the greedy algorithm.Using the property of submodularity of principal points for a multivariate binary distribution,the accuracy of approximations is at least(1-1/e)times the optimal solution proved by Nemhauser et al.Finally, we show the result of an application of the methods to questionnaire survey data.
