I've got a set of data ranging between 0 and 1. Most of the values in this set are extremely small (like, between 0.003 and 10^-7). I want to scale up these values, so they are less small but still between 0 and 1. Furthermore, I want to preserve the order of the set of data (i.e., if a value is bigger than another in the original set, this will still be the case in the new transformed set).
Essentially, this is how the function should go: Input: [0, 1] -> Function -> [0, 1]
I am trying to scale them up using logarithms (because they are increasing functions and they can scale up small values) but am having some difficulty selecting an appropriate base for the logarithm.
Any suggestions?