stringdistmetrics {stringdist}  R Documentation 
String metrics in stringdist
Description
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 humantyped names that may contain typo's, the JaroWinkler 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 DamerauLevenshtein distance). 
lv  Levenshtein distance (as in R's native adist ). 
dl  Full DamerauLevenshtein 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 JaroWinkler distance. 
soundex  Distance based on soundex encoding (see below) 
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 DamerauLevenshtein 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 lcsdistance 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_iy_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 1x\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 1X\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(mt)/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 JaroWinkler distance (method=jw
, 0<p<=0.25
) adds a
correction term to the Jarodistance. It is defined as d  l\cdot p\cdot d
, where
d
is the Jarodistance. 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 'prefix' 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 az and AZ. A warning is emitted when nonprintable or nonascii
characters are encountered. Also see printable_ascii
.
The running_cosine distance is an implementatation of the cosine
distance especially meant for fuzzy text search as in afind
.
In fuzzy search a window of n
characters slides accros a (long)
string while for each position of the window the distance between the part
of the string in the window and a search pattern is computed. The (position
of) the window with the shortest distance to the search pattern is returned.
Sliding the window with a single position only affects the q
grams at
the beginning and end of the window, and the 'running cosine' distance uses
this and a few other tricks to save calculations.
References

MPJ van der Loo (2014) The stringdist package for approximate string matching. The R Journal 6(1) 111122.

L. Boytsov (2011). Indexing methods for approximate dictionary searching: comparative analyses. ACM Journal of experimental algorithmics 16 188.

G. Navarro (2001). A guided tour to approximate string matching. ACM Computing Surveys 33 3188.
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:
stringdistencoding