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Approximate string comparators

TvungenOne, 2012-06-15Lars Marius Garshol, <larsga@bouvet.no>http://twitter.com/larsga

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Approximate string comparators?

• Basically, measures of the similarity between two strings

• Useful in situations where exact match is insufficient– record linkage– search– ...

• Many of these are slow: O(n2)

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Levenshtein

• Also known as edit distance• Measures the number of edit operations

necessary to turn s1 into s2• Edit operations are– insert a character– remove a character– substitute a character

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Levenshtein example

• Levenshtein -> Löwenstein– Levenstein (remove ‘h’)– Lövenstein (substitute ‘ö’)– Löwenstein (substitute ‘w’)

• Edit distance = 3

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Weighted Levenshtein

• Not all edit operations are equal• Substituting “i” for “e” is a smaller edit

than substituting “o” for “k”• Weighted Levenshtein evaluates each

edit operation as a number 0.0-1.0• Difficult to implement– weights are also language-dependent

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Jaro-Winkler

• Developed at the US Bureau of the Census

• For name comparisons– not well suited to long strings– best if given name/surname are separated

• Exists in a few variants– originally proposed by Winkler– then modified by Jaro– a few different versions of modifications etc

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Jaro-Winkler definition

• Formula:– m = number of matching characters– t = number of transposed characters

• A character from string s1 matches s2 if the same character is found in s2 less then half the length of the string away

• Levenshtein ~ Löwenstein = 0.8• Axel ~ Aksel = 0.783

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Jaro-Winkler variant

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Soundex

• A coarse schema for matching names by sound– produces a key from the name– names match if key is the same

• In common use in many places– Nav’s person register uses it for search– built-in in many databases– ...

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Soundex definition

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Examples

• soundex(“Axel”) = ‘A240’• soundex(“Aksel”) = ‘A240’• soundex(“Levenshtein”) = ‘L523’• soundex(“Löwenstein”) = ‘L152’

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Metaphone

• Developed by Lawrence Philips• Similar to Soundex, but much more

complex– both more accurate and more sensitive

• Developed further into Double Metaphone

• Metaphone 3.0 also exists, but only available commercially

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Metaphone examples

• metaphone(“Axel”) = ‘AKSL’• metaphone(“Aksel”) = ‘AKSL’• metaphone(“Levenshtein”) = ‘LFNX’• metaphone(“Löwenstein”) = ‘LWNS’

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Dice coefficient

• A similarity measure for sets– set can be tokens in a string– or characters in a string

• Formula:

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TFIDF

• Compares strings as sets of tokens– a la Dice coefficient

• However, takes frequency of tokens in corpus into account– this matches how we evaluate matches

mentally

• Has done well in evaluations– however, can be difficult to evaluate– results will change as corpus changes

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More comparators

• Smith-Waterman– originated in DNA sequencing

• Q-grams distance– breaks string into sets of pieces of q characters– then does set similarity comparison

• Monge-Elkan– similar to Smith-Waterman, but with affine gap

distances– has done very well in evaluations– costly to evaluate

• Many, many more– ...