5.1 General remarks
In this chapter, the first steps in any analysis of a compositional data set are addressed. The set is represented as a matrix with rows (observed compositions) and columns (parts). An exploratory analysis includes the following steps:
- computing descriptive statistics, that is, the center and variation matrix of a data set, as well as its total variability;
- looking at the biplot of the data set to discover patterns;
- plotting patterns in ternary diagrams of subcompositions, possibly centered to enhance visualization;
- defining an appropriate representation in orthonormal coordinates and computing the corresponding coordinates; and
- computing classical summary statistics of the coordinates and representing the results in a balance-dendrogram.
In general, the last two steps will be based on a particular sequential binary partition, defined either a priori or as a result of the insights provided by the first three steps.
Before starting, some general considerations need to be made. The first step in a statistical analysis is to check the data set for errors. It can be done using standard procedures, for example, using the minimum ...