Levenshtein {comparator} | R Documentation |
Levenshtein String/Sequence Comparator
Description
The Levenshtein (edit) distance between two strings/sequences x
and
y
is the minimum cost of operations (insertions, deletions or
substitutions) required to transform x
into y
.
Usage
Levenshtein(
deletion = 1,
insertion = 1,
substitution = 1,
normalize = FALSE,
similarity = FALSE,
ignore_case = FALSE,
use_bytes = FALSE
)
Arguments
deletion |
positive cost associated with deletion of a character or sequence element. Defaults to unit cost. |
insertion |
positive cost associated insertion of a character or sequence element. Defaults to unit cost. |
substitution |
positive cost associated with substitution of a character or sequence element. Defaults to unit cost. |
normalize |
a logical. If TRUE, distances are normalized to the unit interval. Defaults to FALSE. |
similarity |
a logical. If TRUE, similarity scores are returned instead of distances. Defaults to FALSE. |
ignore_case |
a logical. If TRUE, case is ignored when comparing strings. |
use_bytes |
a logical. If TRUE, strings are compared byte-by-byte rather than character-by-character. |
Details
For simplicity we assume x
and y
are strings in this section,
however the comparator is also implemented for more general sequences.
A Levenshtein similarity is returned if similarity = TRUE
, which
is defined as
\mathrm{sim}(x, y) = \frac{w_d |x| + w_i |y| - \mathrm{dist}(x, y)}{2},
where |x|
, |y|
are the number of characters in x
and
y
respectively, \mathrm{dist}
is the Levenshtein distance,
w_d
is the cost of a deletion and w_i
is the cost of an
insertion.
Normalization of the Levenshtein distance/similarity to the unit interval
is also supported by setting normalize = TRUE
. The normalization approach
follows Yujian and Bo (2007), and ensures that the distance remains a metric
when the costs of insertion w_i
and deletion w_d
are equal.
The normalized distance \mathrm{dist}_n
is defined as
\mathrm{dist}_n(x, y) = \frac{2 \mathrm{dist}(x, y)}{w_d |x| + w_i |y| + \mathrm{dist}(x, y)},
and the normalized similarity \mathrm{sim}_n
is defined as
\mathrm{sim}_n(x, y) = 1 - \mathrm{dist}_n(x, y) = \frac{\mathrm{sim}(x, y)}{w_d |x| + w_i |y| - \mathrm{sim}(x, y)}.
Value
A Levenshtein
instance is returned, which is an S4 class inheriting from
StringComparator
.
Note
If the costs of deletion and insertion are equal, this comparator is
symmetric in x
and y
. In addition, the normalized and
unnormalized distances satisfy the properties of a metric.
References
Navarro, G. (2001), "A guided tour to approximate string matching", ACM Computing Surveys (CSUR), 33(1), 31-88.
Yujian, L. & Bo, L. (2007), "A Normalized Levenshtein Distance Metric", IEEE Transactions on Pattern Analysis and Machine Intelligence 29, 1091–1095.
See Also
Other edit-based comparators include Hamming
, LCS
,
OSA
and DamerauLevenshtein
.
Examples
## Compare names with potential typos
x <- c("Brian Cheng", "Bryan Cheng", "Kondo Onyejekwe", "Condo Onyejekve")
pairwise(Levenshtein(), x, return_matrix = TRUE)
## When the substitution cost is high, Levenshtein distance reduces to LCS distance
Levenshtein(substitution = 100)("Iran", "Iraq") == LCS()("Iran", "Iraq")