Correspondence analysis has found extensive use in the social and environmental sciences as a method for visualizing the patterns of association in a table of frequencies. Inherent to the method is the expression of the frequencies in each row or each column relative to their respective totals,...

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original...

The case of two transition tables is considered, that is two square asymmetric matrices of frequencies where the rows and columns of the matrices are the same objects observed at three different time points. Different ways of visualizing the tables, either separately or jointly, are examined. We...

The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational...

We compare two methods for visualising contingency tables and develop a method called the ratio map which combines the good properties of both. The first is a biplot based on the logratio approach to compositional data analysis. This approach is founded on the principle of subcompositional...

The use of simple and multiple correspondence analysis is well-established in social science research for understanding relationships between two or more categorical variables. By contrast, canonical correspondence analysis, which is a correspondence analysis with linear restrictions on the...

Correspondence analysis is introduced in the brand association literature as an alternative tool to measure dominance, for the particular case of free choice data. The method is also used to analyse differences, or asymmetries, between brand-attribute associations where attributes are associated...

The singular value decomposition and its interpretation as a linear biplot has proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the specific case of compositional data consisting of positive vectors each of which is constrained to...

Because of its many advantages, the use of decision trees has become an increasingly popular alternative predictive tool for building classification and regression models. Its origins date back for about five decades where the algorithm can be broadly described by repeatedly partitioning the...

Most methods of multivariate analysis rely on a measure of proximity between individual cases or samples to quantify inter-sample differences. The choice of this measure is fundamental to the method and its subsequent results. For example, when data are abundance counts of a set of species at...