DamerauLevenshtein {comparator}

Damerau-Levenshtein String/Sequence Comparator

Description

The Damerau-Levenshtein distance between two strings/sequences x and y is the minimum cost of operations (insertions, deletions, substitutions or transpositions) required to transform x into y. It differs from the Levenshtein distance by including transpositions (swaps) among the allowable operations.

Usage

DamerauLevenshtein(
  deletion = 1,
  insertion = 1,
  substitution = 1,
  transposition = 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.

transposition

positive cost associated with transposing (swapping) a pair of characters or sequence elements. 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 Damerau-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 Damerau-Levenshtein distance, w_d is the cost of a deletion and w_i is the cost of an insertion.

Normalization of the Damerau-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 DamerauLevenshtein instance is returned, which is an S4 class inheriting from Levenshtein.

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

Boytsov, L. (2011), "Indexing methods for approximate dictionary searching: Comparative analysis", ACM J. Exp. Algorithmics 16, Article 1.1.

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, Levenshtein and OSA.

Examples

## The Damerau-Levenshtein distance reduces to ordinary Levenshtein distance 
## when the cost of transpositions is high
x <- "plauge"; y <- "plague"
DamerauLevenshtein(transposition = 100)(x, y) == Levenshtein()(x, y)

## Compare car names using normalized Damerau-Levenshtein similarity
data(mtcars)
cars <- rownames(mtcars)
pairwise(DamerauLevenshtein(similarity = TRUE, normalize=TRUE), cars)

## Compare sequences using Damerau-Levenshtein distance
x <- c("G", "T", "G", "C", "T", "G", "G", "C", "C", "C", "A", "T")
y <- c("G", "T", "G", "C", "G", "T", "G", "C", "C", "C", "A", "T")
DamerauLevenshtein()(list(x), list(y))