问题
If the Levenshtein distance between two strings, s and t is given by L(s,t),
what is the difference in the impact on the resulting heuristic of the following two different normalization schemes?
L(s,t) / [length(s) + length(t)]L(s,t) / max[length(s), length(t)](L(s,t)*2) / [length(s) + length(t)]
I noticed that normalization approach 2 is recommended by the Levenshtein distance Wikipedia page but no mention is made of approach 1. Are both approaches equally valid? Just wondering if there is some mathematical justification for using one over the other.
Also, what is the difference between approach 1 and approach 3?
With the following example:
s = "Hi, my name is"
t = "Hello, my name is"
L(s,t) = 4
length(s) = 14 (includes white space)
length(t) = 17 (includes white space)
The Levenshtein distance given the three normalization algorithms above are:
4/(14+17) = 0.129
4/(17) = 0.235
(4*2)/(14+17) = 0.258
回答1:
The effects of both variants should be nearly the same. The second term covers a range from zero (strings are equal) to one (completely different) while the upper range in the first variant depends on the length of the strings. If the lengths are nearly equal the upper bound is 0.5 and increases on larger differences between the lengths.
来源：https://stackoverflow.com/questions/41066394/difference-in-normalization-of-levenshtein-edit-distance