Edit distance
In computer science, edit distance is a way of quantifying how dissimilar two strings (e.g., words) are to one another by counting the minimum number of operations required to transform one string into the other. Edit distances find applications in natural language processing, where automatic spelling correction can determine candidate corrections for a misspelled word by selecting words from a dictionary that have a low distance to the word in question. In bioinformatics, it can be used to quantify the similarity of DNA sequences, which can be viewed as strings of the letters A, C, G and T.
Different definitions of an edit distance use different sets of string operations. The Levenshtein distance operations are the removal, insertion, or substitution of a character in the string. Being the most common metric, the Levenshtein distance is usually what is meant by "edit distance".
Given two strings a and b on an alphabet Σ (e.g. the set of ASCII characters, the set of bytes [0..255], etc.), the edit distance d(a, b) is the minimum-weight series of edit operations that transforms a into b. One of the simplest sets of edit operations is that defined by Levenshtein in 1966:
In Levenshtein's original definition, each of these operations has unit cost (except that substitution of a character by itself has zero cost), so the Levenshtein distance is equal to the minimum number of operations required to transform a to b. A more general definition associates non-negative weight functions wins(x), wdel(x) and wsub(x, y) with the operations.
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