An Algorithm for Principal Points Considering External Criterion for Multivariate Binary Distributions

Abstract

The concept of principal points has been the subject of numerous theoretical and application studies. There are also the studies of principal points for multivariate binary distributions. Moreover, , recently, principal points for multivariate binary distribution considering two classes using an external criterion has studied. For example binary questionnaire data for products or services are classified based on the external criterion of customer satisfaction. In previous studies, principal points were located by minimizing the expected squared distance between the principal points and a multivariate binary distribution within a class, and maximizing the squared distance between the two classes. However, this approach to finding principal points was very time-consuming. In this study, we propose an algorithm for finding principal points considering an external criterion for multivariate binary distributions. Moreover, we apply our method to real binary data that is divided into two classes by the binary criterion, and we demonstrate the effectiveness of our approach.