TWO CLASSIFICATION TECHNIQUES OF 3-WAY DISCRETE DATA

-QUANTIFICATION BY MEANS OF CORRELATION RATIO AND THREE-DIMENSIONAL CORRELATION COEFFICIENT-

Abstract

Two new classification methods are proposed to find out clusters from 3-way discrete data. They are quantification methods using the criteria maximizing correlation ratio and three-dimensional correlation coefficient, which lead to solving eigenequations. Threedimensional correlation coefficient is defined by E?{(X-E(X))(Y-E(Y))(Z-E(Z))}/√E(X-E(X)) ²E(Y-E(Y)) ²E(Z-E(Z)) ², which is convenient to estimate the degree of joint relation among three variables of 3-way data. Some properties of three-dimensional correlation coefficient are given. Results of applying the methods to small data are also presented.