Two Experiments are reported on in the paper On order equivalences between distance and similarity measures on sequences and trees Martin Emms and Hector-Hugo Franco-Penya Proceedings of ICPRAM 2012 International Conference on Pattern Recognition Application and Methods FIRST EXPERIMENT **************** this concernns converting a distance setting into a variety of similarity settings. All the similarity settings are A-duals of the distance setting the distance setting is: distab(x,[]) : 1 distab(x,y) : 1 distab(x,x) : 0 various dual similarity settings derive from this by setting delta in (i) conversion of Lemma 1: simitab(x,[]) : 1 - delta/2 simitab(x,y) : delta - 1 simitab(x,x) : delta delta values 2 1.5 1 0.5 0.2 0.1 The nodes in the trees have multi-part labels. For this experiment, swap cost on two nodes is 2-valued, and nodes just treated as identical or not. SECOND EXPERIMENT This experiment starts out with similarity setting and derives various distance settings by conversion (ii) of Lemma 1. The similarity setting is sim(x,[]) = 0.5 sim(x,y) = 1 - ham(x,y) See later section for further info on how ham(x,y) is defined. Transformation (ii) from Lemma 2, gives distance settings: dis(x,[]) = sim(x,[]) + delta/2 = 0.5 + delta/2 dis(x,y) = delta - sim(x,y) = delta - 1 + ham(x,y) = ham(x,y) + (delta-1) Did this for delta = 1.0 1.5 2.0 2.5 3.0 3.5 4.0