The analysis based on principal matrix decomposition for 3-mode binary data

摘要

Recently, principal points for a multivariate binary distribution (Yamashita and Suzuki, 2014, 2015) have been proposed as the binary vectors that optimally represent a distribution, in terms of the average Euclidian squared distance between a multivariate binary distribution and the vectors. In this paper, we proposes a new analysis procedure for 3-mode binary data, based on principal points for a multivariate binary distribution (Yamashita and Suzuki, 2014, 2015). Moreover, we propose a method that decomposes principal matrixes for 3-mode binary data into a small number of vectors based on vector products. In order to investigate our method's applicability to real-world data, we use the method to analyse 3-mode structured data from annual all-star games for Japanese professional baseball.