Information Retrieval and Organisation
                                                    Dell Zhang

Edit Distance

The (minimum) edit distance between two strings s1 and s2 is the minimum number of basic operations to convert s1 to s2.

Levenshtein-Distance

􏰀 Levenshtein distance: the admissible basic operations are: insert, delete, and replace 􏰀 Levenshtein distance dog→do: 1 (deletion) 􏰀 Levenshtein distance cat→cart: 1 (insertion) 􏰀 Levenshtein distance cat→cut: 1 (replacement) 􏰀 Levenshtein distance cat→act: 2 (2 replacements or 1 insertion and 1 deletion)

Computing Distance

Image Source!

Each cell will contain

 the (cheapest) cost of getting
 from the string on the left-hand side to the string on the right-hand side

􏰀We know the costs for

the uppermost row and the leftmost column:

􏰀 we have to get from “” to GEORDIE by inserting characters

􏰀 we have to get from GEORGE to “” by deleting characters

(C)	(B)
(A)	*

For other cells, take the minimum of costs

􏰀 Coming from (A): 􏰀 add 1 to cost in (A) — (insertion)

􏰀 Coming from (B): 􏰀 add 1 to cost in (B) — (deletion)

􏰀 Coming from (C): 􏰀 if characters in row and column are equal, copy cost from (c) 􏰀 otherwise, add 1 to cost in (C) — (replacement)