Multidimensional Interval-Data: Metrics and Factorial Analysis

Statistical units described by interval-valued variables represent a special case of Symbolic Objects, where all descriptors are quantitative variables. In this context, the paper presents two different metrics in R for interval-valued data that are based on the definition of the Hausdorff distance in R. Hausdorff distance in R (for any p ≥ 1) is a L∞ norm between pairs of closed sets. However, when p > 1 the problem complexity leads towards the definition of L2 norms approximating as well as possible the Hausdorff distance. Given a set of n units described by p interval-valued variables, we compute and represent the distances over factorial planes that are defined by factorial analyses that are consistent with the two distance measure definitions.