How do I convert between a measure of similarity a

Question

Is there a general way to convert between a measure of similarity and a measure of distance?

Consider a similarity measure like the number of 2-grams that two strings have in common.

2-grams('beta', 'delta') = 1
2-grams('apple', 'dappled') = 4

What if I need to feed this to an optimization algorithm that expects a measure of difference, like Levenshtein distance?

This is just an example...I'm looking for a general solution, if one exists. Like how to go from Levenshtein distance to a measure of similarity?

I appreciate any guidance you may offer.

Answer 1

If your similarity measure (s) is between 0 and 1, you can use one of these:

1-s
sqrt(1-s)
-log(s)
(1/s)-1