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...

The book "Mathematics and Archaeology", consisting of 25 chapters by a range of international scholars in archaeology, will be published by Chapman & Hall in 2014. The present document, written as an invited Epilogue to the book, recounts the rediscovery of the book 275 years later by an...

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of...

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example,...

The problem of outliers is well-known in statistics: an outlier is a value that is far from the general distribution of the other observed values, and can often perturb the results of a statistical analysis. Various procedures exist for identifying outliers, in case they need to receive special...

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...

In order to interpret the biplot it is necessary to know which points – usually variables – are the ones that are important contributors to the solution, and this information is available separately as part of the biplot’s numerical results. We propose a new scaling of the display, called...

Perceptual maps have been used for decades by market researchers to illuminate them about the similarity between brands in terms of a set of attributes, to position consumers relative to brands in terms of their preferences, or to study how demographic and psychometric variables relate to...

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...