# stringdist-metrics

##### String metrics in stringdist

This page gives an overview of the string dissimilarity measures offered by stringdist.

##### String Metrics

String metrics are ways of quantifying the dissimilarity between two finite sequences, usually text strings. Over the years, many such measures have been developed. Some are based on a mathematical understanding of the set of all strings that can be composed from a finite alphabet, others are based on more heuristic principles, such as how a text string sounds when pronounced by a native English speaker.

The terms 'string metrics' and 'string distance' are used more or less interchangibly in literature. From a mathematical point of view, string metrics often do not obey the demands that are usually required from a distance function. For example, it is not true for all string metrics that a distance of 0 means that two strings are the same (e.g. in the \(q\)-gram distance). Nevertheless, string metrics are very useful in practice and have many applications.

The metric you need to choose for an application strongly depends on both the nature of the string (what does the string represent?) and the cause of dissimilarities between the strings you are measuring. For example, if you are comparing human-typed names that may contain typo's, the Jaro-Winkler distance may be of use. If you are comparing names that were written down after hearing them, a phonetic distance may be a better choice.

Currently, the following distance metrics are supported by stringdist.

Method name |
Description |

`osa` |
Optimal string aligment, (restricted Damerau-Levenshtein distance). |

`lv` |
Levenshtein distance (as in R's native `adist` ). |

`dl` |
Full Damerau-Levenshtein distance. |

`hamming` |
Hamming distance (`a` and `b` must have same nr of characters). |

`lcs` |
Longest common substring distance. |

`qgram` |
\(q\)-gram distance. |

`cosine` |
cosine distance between \(q\)-gram profiles |

`jaccard` |
Jaccard distance between \(q\)-gram profiles |

`jw` |
Jaro, or Jaro-Winker distance. |

##### A short description of string metrics supported by stringdist

See Van der Loo (2014) for an extensive description and references. The review papers of Navarro (2001) and Boytsov (2011) provide excellent technical overviews of respectively online and offline string matching algorithms.

The **Hamming distance** (`method='hamming'`

) counts the number of
character substitutions that turns `b`

into `a`

. If `a`

and `b`

have different number of characters the distance is `Inf`

.

The **Levenshtein distance** (`method='lv'`

) counts the number of
deletions, insertions and substitutions necessary to turn `b`

into
`a`

. This method is equivalent to `R`

's native `adist`

function.

The **Optimal String Alignment distance** (`method='osa'`

) is like the Levenshtein
distance but also allows transposition of adjacent characters. Here, each
substring may be edited only once. (For example, a character cannot be transposed twice
to move it forward in the string).

The **full Damerau-Levensthein distance** (`method='dl'`

) is like the optimal
string alignment distance except that it allows for multiple edits on substrings.

The **longest common substring** (method='lcs') is defined as the longest string that can be
obtained by pairing characters from `a`

and `b`

while keeping the order
of characters intact. The **lcs-distance** is defined as the number of unpaired characters.
The distance is equivalent to the edit distance allowing only deletions and insertions,
each with weight one.

A **\(q\)-gram** (method='qgram') is a subsequence of \(q\) *consecutive*
characters of a string. If \(x\) (\(y\)) is the vector of counts
of \(q\)-gram occurrences in `a`

(`b`

), the **\(q\)-gram distance**
is given by the sum over the absolute differences \(|x_i-y_i|\).
The computation is aborted when `q`

is is larger than the length of
any of the strings. In that case `Inf`

is returned.

The **cosine distance** (method='cosine') is computed as \(1-x\cdot y/(\|x\|\|y\|)\), where \(x\) and
\(y\) were defined above.

Let \(X\) be the set of unique \(q\)-grams in `a`

and \(Y\) the set of unique
\(q\)-grams in `b`

. The **Jaccard distance** (`method='jaccard'`

) is given by \(1-|X\cap Y|/|X\cup Y|\).

The **Jaro distance** (`method='jw'`

, `p=0`

), is a number
between 0 (exact match) and 1 (completely dissimilar) measuring
dissimilarity between strings. It is defined to be 0 when both strings have
length 0, and 1 when there are no character matches between `a`

and
`b`

. Otherwise, the Jaro distance is defined as
\(1-(1/3)(w_1m/|a| + w_2m/|b| + w_3(m-t)/m)\).
Here,\(|a|\) indicates the number of characters in `a`

, \(m\) is
the number of character matches and \(t\) the number of transpositions of
matching characters. The \(w_i\) are weights associated with the characters
in `a`

, characters in `b`

and with transpositions. A character
\(c\) of `a`

*matches* a character from `b`

when \(c\)
occurs in `b`

, and the index of \(c\) in `a`

differs less than
\(\max(|a|,|b|)/2 -1\) (where we use integer division) from the index of
\(c\) in `b`

. Two matching characters are transposed when they are
matched but they occur in different order in string `a`

and `b`

.

The **Jaro-Winkler distance** (`method=jw`

, `0<p<=0.25`

) adds a
correction term to the Jaro-distance. It is defined as \(d - l\cdot p\cdot d\), where
\(d\) is the Jaro-distance. Here, \(l\) is obtained by counting, from
the start of the input strings, after how many characters the first
character mismatch between the two strings occurs, with a maximum of four. The
factor \(p\) is a penalty factor, which in the work of Winkler is often
chosen \(0.1\).

For the **soundex** distance (method='soundex'), strings are translated to a soundex code
(see `phonetic`

for a specification). The
distance between strings is 0 when they have the same soundex code,
otherwise 1. Note that soundex recoding is only meaningful for characters
in the ranges a-z and A-Z. A warning is emitted when non-printable or non-ascii
characters are encountered. Also see `printable_ascii`

.

##### References

MPJ van der Loo (2014)

*The stringdist package for approximate string matching*. The R Journal**6**(1) 111-122.L. Boytsov (2011).

*Indexing methods for approximate dictionary searching: comparative analyses*. ACM Journal of experimental algorithmics**16**1-88.G. Navarro (2001).

*A guided tour to approximate string matching*. ACM Computing Surveys**33**31-88.

##### See Also

Functions applying string metrics to text:

`stringdist`

,`stringdistmatrix`

,`amatch`

Functions applying string metrics to integer sequences:

`seq_dist`

,`seq_distmatrix`

,`seq_amatch`

Encoding issues:

`stringdist-encoding`

*Documentation reproduced from package stringdist, version 0.9.4.6, License: GPL-3*