Abstract: Given two distances d and d′ defined on a finite set I, with d  d′, we characterise the set of all ultrametrics lying between d and d′ (if any), showing they are the union of finitely many intervals with a common top endpoint, the subdominant ultrametric of d′. We also provide an algorithm to compute the bottom of any interval, given by any upperminimal ultrametric of d less than d′. A series of approximations according to the supremum norm derive from this.

Keywords: ultrametric, subdominant ultrametric, upperminimal ultrametrics, approximation, supremum norm

MSC: G3: Statistics

Link:

INTERVALS AS ULTRAMETRIC APPROXIMATIONS ACCORDING TO THE SUPREMUM NORM

Bernard Fichet

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p13.pdf