How do I convert between a measure of similarity and a measure of difference (distance)?

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 ha

Answer 1

Let d denotes distance, s denotes similarity. To convert distance measure to similarity measure, we need to first normalize d to [0 1], by using d_norm = d/max(d). Then the similarity measure is given by:

s = 1 - d_norm.

where s is in the range [0 1], with 1 denotes highest similarity (the items in comparison are identical), and 0 denotes lowest similarity (largest distance).