Principal component analysis for interval data: common approaches and variations

In real life there are many kinds of phenomena that are better described by interval bounds than by single-valued variables. In fact, intervals take into account the imprecision due to measurement errors. When there is information about the imprecision distribution the fuzzy data coding is used to represent the imprecision. In this paper, we first review the main dimension reduction techniques for interval-valued data and then we propose a midpoints and radii-based approach. In particular, an alternative pre-processing and Procrustean rotation of the traditional midpoints and radii approach is proposed