Principal component analysis of interval data: a symbolic data analysis approach
Statistical methods have been mainly developed for the analysis of single-valued variables. However, in real life there are many situations in which the use of these variables may cause severe loss of information. Dealing with quantitative variables, there are many cases in which a more complete information can be surely achieved by describing a set of statistical units in terms of interval data. Most widely used approaches to interval data analysis treat intervals as spread ranges with respect to a central value. The spread is generally assumed as the consequence of a measurement error and is considered as a perturbation in the data. The present paper deals with the study of continuous interval data by means of suitable principal components analyses. Statistical units described by interval variables can be considered as special cases of symbolic data, in which only quantitative variables are considered. Moreover, the symbolic data approach for the interval data treatment offers many useful tools that can be helpful in the interpretation of results. Also, in the present paper, some extensions of the principal components analyses are proposed with the aim of representing, in a space of reduced dimension, images of the hypercubes, as these data are represented, pointing out differences and similarities according to their structural features.
scientific article; zbMATH DE number 1524257