OSA {comparator} R Documentation

## Optimal String Alignment (OSA) String/Sequence Comparator

### Description

The Optimal String Alignment (OSA) 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, subject to the constraint that no substring/subsequence is edited more than once.

### Usage

OSA(
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.

An OSA 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, dist is the OSA distance, w_d is the cost of a deletion and w_i is the cost of an insertion.

Normalization of the OSA 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

An OSA 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. The OSA distance is not a proper metric as it does not satisfy the triangle inequality. The Damerau-Levenshtein distance is closely related—it allows the same edit operations as OSA, but removes the requirement that no substring can be edited more than once.

### 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.

Other edit-based comparators include Hamming, LCS, Levenshtein and DamerauLevenshtein.

### Examples

## Compare strings with a transposition error
x <- "plauge"; y <- "plague"
OSA()(x, y) != Levenshtein()(x, y)

## Unlike Damerau-Levenshtein, OSA does not allow a substring to be
## edited more than once
x <- "ABC"; y <- "CA"
OSA()(x, y) != DamerauLevenshtein()(x, y)

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



[Package comparator version 0.1.2 Index]