The experiment settings

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



Martin Emms
2012-08-28