http://en.wikipedia.org/wiki/BM25

http://xapian.org/docs/bm25.html

http://en.wikipedia.org/wiki/Levenshtein_distance

In information theory and computer science, the Levenshtein distance is a metric for measuring the amount of difference between two sequences (i.e., the so called edit distance). The Levenshtein distance between two strings is given by the minimum number of operations needed to transform one string into the other, where an operation is an insertion, deletion, or substitution of a single character. A generalization of the Levenshtein distance (Damerau-Levenshtein distance) allows the transposition of two characters as an operation.

The metric is named after Vladimir Levenshtein, who considered this distance in 1965.^[1] It is often used in applications that need to determine how similar, or different, two strings are, such as spell checkers.

http://xapian.org/docs/bm25.html

The tf–idf weight (term frequency–inverse document frequency) is a weight often used in information retrieval and text mining. This weight is a statistical measure used to evaluate how important a word is to a document in a collection or corpus. The importance increases proportionally to the number of times a word appears in the document but is offset by the frequency of the word in the corpus. Variations of the tf–idf weighting scheme are often used by search engines as a central tool in scoring and ranking a document’s relevance given a user query.