An Alternative to Correspondence Analysis Using Hellinger Distance.

Abstract : In this paper, a general theory of canonical coordinates is developed for reduction of dimensionality in multivariate data, assessing the loss of information and plotting higher dimensional data in two or three dimensions for visual displays. The theory is applied to data in two way tables with variables in one category and samples (individual or populations) in the other. The method is applicable to data with continuous measurements on the variables as well as to frequencies of attributes. An alternative distance is suggested. The new method has some attractive features and does not suffer from some inherent drawbacks resulting from the use of the chi-square distance and variable sample sizes for the populations in the correspondence analysis. The technique of biplots where the populations and the variables are represented on the same chart is discussed.