Canonical Coordinates for Graphical Representation of Multivariate Data

摘要

A general theory is developed for representing population profiles characterizedby multiple measurements in a low dimensional Euclidean space. The basic inputs of the problem are a matrix of distances between population profiles and the weights to be attached to different population profiles. The derived coordinates in the reduced space are called canonical coordinates. A well known method for representing row or column profiles in a contingency table using a chisquare type distance between profiles is the correspondence analysis. It is suggested that a similar analysis based on Hellinger distance between profiles has some advantages and is better suited for studying the configuration of profiles. An asymmetric biplot technique which is useful in interpreting differences in row (column) profiles in terms of column (row) categories is developed.