Normalized k-means clustering of hyper-rectangles

Interval variables can be measured on very different scales. We first remind a general methodology used for measuring the dispersion of a variable from an optimal center and we define two measures of dispersions associated to two optimal "centers" for interval variables. Then we study the relations between the standardization of a data table and the use in clustering of a normalized distance. Finally we define two normalized distances between hyper-rectangles and their use in two normalized k-means clustering algorithms.