## Fuzzinessedit

Fuzzy matching treats two words that are “fuzzily” similar as if they were the same word. First, we need to define what we mean by fuzziness.

In 1965, Vladimir Levenshtein developed the Levenshtein distance, which measures the number of single-character edits required to transform one word into the other. He proposed three types of one-character edits:

• Substitution of one character for another: _f_ox → _b_ox
• Insertion of a new character: sic → sic_k_
• Deletion of a character: b_l_ack → back

Frederick Damerau later expanded these operations to include one more:

• Transposition of two adjacent characters: _st_ar → _ts_ar

For example, to convert the word `bieber` into `beaver` requires the following steps:

1. Substitute `v` for `b`: bie_b_er → bie_v_er
2. Substitute `a` for `i`: b_i_ever → b_a_ever
3. Transpose `a` and `e`: b_ae_ver → b_ea_ver

These three steps represent a Damerau-Levenshtein edit distance of 3.

Clearly, `bieber` is a long way from `beaver`—they are too far apart to be considered a simple misspelling. Damerau observed that 80% of human misspellings have an edit distance of 1. In other words, 80% of misspellings could be corrected with a single edit to the original string.

Elasticsearch supports a maximum edit distance, specified with the `fuzziness` parameter, of 2.

Of course, the impact that a single edit has on a string depends on the length of the string. Two edits to the word `hat` can produce `mad`, so allowing two edits on a string of length 3 is overkill. The `fuzziness` parameter can be set to `AUTO`, which results in the following maximum edit distances:

• `0` for strings of one or two characters
• `1` for strings of three, four, or five characters
• `2` for strings of more than five characters

Of course, you may find that an edit distance of `2` is still overkill, and returns results that don’t appear to be related. You may get better results, and better performance, with a maximum `fuzziness` of `1`.