Levenshtein distance: how to better handle words swapping positions?

Question

I\'ve had some success comparing strings using the PHP levenshtein function.

However, for two strings which contain substrings that have swapped positions, the algorithm

Answer 1

N-grams

Use N-grams, which support multiple-character transpositions across the whole text.

The general idea is that you split the two strings in question into all the possible 2-3 character substrings (n-grams) and treat the number of shared n-grams between the two strings as their similarity metric. This can be then normalized by dividing the shared number by the total number of n-grams in the longer string. This is trivial to calculate, but fairly powerful.

For the example sentences:

A. The quick brown fox
B. brown quick The fox
C. The quiet swine flu

A and B share 18 2-grams

A and C share only 8 2-grams

out of 20 total possible.

This has been discussed in more detail in the Gravano et al. paper.

tf-idf and cosine similarity

A not so trivial alternative, but grounded in information theory would be to use term term frequency–inverse document frequency (tf-idf) to weigh the tokens, construct sentence vectors and then use cosine similarity as the similarity metric.

The algorithm is:

1. Calculate 2-character token frequencies (tf) per sentence.
2. Calculate inverse sentence frequencies (idf), which is a logarithm of a quotient of the number of all sentences in the corpus (in this case 3) divided by the number of times a particular token appears across all sentences. In this case th is in all sentences so it has zero information content (log(3/3)=0).
3. Produce the tf-idf matrix by multiplying corresponding cells in the tf and idf tables.
4. Finally, calculate cosine similarity matrix for all sentence pairs, where A and B are weights from the tf-idf table for the corresponding tokens. The range is from 0 (not similar) to 1 (equal).
   
   

Levenshtein modifications and Metaphone

Regarding other answers. Damerau–Levenshtein modificication supports only the transposition of two adjacent characters. Metaphone was designed to match words that sound the same and not for similarity matching.