Hi guys ,
I've used a structural distance-based measure to compute similarity between each pair of nodes in an undirect graph. Hence, I calculated a distance matrix "D" such that the distance value "Dij" is simply the shortest-path between node i and node j. However, obtained distance values are absolutes (i.e. 5, 19, 3...etc) and I'd like to normalize them, such that : 0
You can do something like this for example (just a neutral normalization function):
Instead of 1 use 100 (as a percentage: 100%)
As 0 use 0 (0%)
Now calculate the scale of your real values interval:
s = highest similarity value - smallest similarity value
Then the rescaled value differences are rij=(100*dij) / s
dij are the value differences between every consecutive pair of similarity values (this means that j=i+1)
To consecutively get each rescaled value you just have to add the correspondent value difference to the previous value (starting from 0)
For example, if your similarities were: (50, 150, 200, 400)
you would have:
s=350
rij=(100*dij) / 350
The dij's and rij's are:
d01=100; d12=50; d23=200
r01=28.57; r12=14.29; r23=57.14
And then finally
r0=0
r1=r0+r01=28.57
r2=r1+r12=42.86
r3=r2+r23=100
These r's are percentages so you just have to divide them by 100 to get your values back in the interval 0..1
Good luck.
There are many transformations between resemblance measures
http://vlado.fmf.uni-lj.si/vlado/papers/Compare.pdf
http://www.liga.ens.fr/~deza/1-59.pdf
For example you can use
s(i,j) = 1/(1+D(i,j))
d(i,j) = 1-s(i,j) = D(i,j)/(1+D(i,j))
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