I am trying to get a continuous mapping from (0,∞) to (0,1). What would be a good mapping?
I need to rank tuples based on values of two of their attributes
a increases very steeply and
b much slower. To accomodate both of them in ranking, I am generating
c=a*b and am using that for ranking. c could vary from sub-1 values to a few billions. this makes comparison very difficult. I tried log10(c)..while that helps in reducing the range significantly, having a proper way to map the values to (0,1) would help. I am trying to look for a function to map c to (0,1) that would have a good spread over entire range of the iterval (0,1).I considered sigmoid, but then I thought since all values are psoitive, sigmoid values would be restricted to (0.5,1)..so had to drop that idea..