String metric

In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("inverse similarity") between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric (e.g. in contrast to string matching) is fulfillment of the triangle inequality. For example, the strings "Sam" and "Samuel" can be considered to be close.^[1] A string metric provides a number indicating an algorithm-specific indication of distance.

The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance).^[2] It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another. Simplistic string metrics such as Levenshtein distance have expanded to include phonetic, token, grammatical and character-based methods of statistical comparisons.

String metrics are used heavily in information integration and are currently used in areas including fraud detection, fingerprint analysis, plagiarism detection, ontology merging, DNA analysis, RNA analysis, image analysis, evidence-based machine learning, database data deduplication, data mining, incremental search, data integration, malware detection,^[3] and semantic knowledge integration.

List of string metrics

Levenshtein distance, or its generalization edit distance
Damerau–Levenshtein distance
Sørensen–Dice coefficient
Block distance or L1 distance or City block distance
Hamming distance
Simple matching coefficient (SMC)
Jaccard similarity or Jaccard coefficient or Tanimoto coefficient
Tversky index
Overlap coefficient
Variational distance^[4]
Hellinger distance or Bhattacharyya distance
Information radius (Jensen–Shannon divergence)
Skew divergence^[4]
Confusion probability^[4]
Tau metric, an approximation of the Kullback–Leibler divergence
Fellegi and Sunters metric (SFS)^[4]
Maximal matches^[4]
Grammar-based distance^[5]
TFIDF distance metric^[6]

There also exist functions which measure a dissimilarity between strings, but do not necessarily fulfill the triangle inequality, and as such are not metrics in the mathematical sense. An example of such function is the Jaro–Winkler distance.

Selected string measures examples

Name	Description	Example
Hamming distance	Only for strings of the same length. Number of changed characters.	"karolin" and "kathrin" is 3.
Levenshtein distance and Damerau–Levenshtein distance	Generalization of Hamming distance that allows for different length strings, and (with Damerau) for transpositions	kitten and sitting have a distance of 3. kitten → sitten (substitution of "s" for "k") sitten → sittin (substitution of "i" for "e") sittin → sitting (insertion of "g" at the end).
Jaro–Winkler distance		JaroWinklerDist("MARTHA","MARHTA") = $d_{j}={\frac {1}{3}}\left({\frac {m}{\|s_{1}\|}}+{\frac {m}{\|s_{2}\|}}+{\frac {m-t}{m}}\right)={\frac {1}{3}}\left({\frac {6}{6}}+{\frac {6}{6}}+{\frac {6-{\frac {2}{2}}}{6}}\right)=0.944$ $m$ is the number of matching characters; $t$ is half the number of transpositions(`"MARTHA"[3]!=H, "MARHTA"[3]!=T`).
Most frequent k characters		MostFreqKeySimilarity('research', 'seeking', 2) = 2

References

^ Lu, Jiaheng; et al. (2013). "String similarity measures and joins with synonyms". Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data. pp. 373–384. doi:10.1145/2463676.2465313. ISBN 9781450320375. S2CID 2091942.
^ Navarro, Gonzalo (2001). "A guided tour to approximate string matching". ACM Computing Surveys. 33 (1): 31–88. doi:10.1145/375360.375365. hdl:10533/172862. S2CID 207551224.
^ Shlomi Dolev; Mohammad, Ghanayim; Alexander, Binun; Sergey, Frenkel; Yeali, S. Sun (2017). "Relationship of Jaccard and edit distance in malware clustering and online identification". 16th IEEE International Symposium on Network Computing and Applications: 369–373.
^ ^a ^b ^c ^d ^e Sam's String Metrics - Computational Linguistics and Phonetics
^ Russell, David J., et al. "A grammar-based distance metric enables fast and accurate clustering of large sets of 16S sequences." BMC bioinformatics 11.1 (2010): 1-14.
^ Cohen, William; Ravikumar, Pradeep; Fienberg, Stephen (2003-08-01). "A Comparison of String Distance Metrics for Name-Matching Tasks": 73–78. {{cite journal}}: Cite journal requires |journal= (help)

External links

String Similarity Metrics for Information Integration A fairly complete overview Archive index at the Wayback Machine
Carnegie Mellon University open source library
StringMetric project a Scala library of string metrics and phonetic algorithms
Natural project a JavaScript natural language processing library which includes implementations of popular string metrics

[1] Lu, Jiaheng; et al. (2013). "String similarity measures and joins with synonyms". Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data. pp. 373–384. doi:10.1145/2463676.2465313. ISBN 9781450320375. S2CID 2091942.

[2] Navarro, Gonzalo (2001). "A guided tour to approximate string matching". ACM Computing Surveys. 33 (1): 31–88. doi:10.1145/375360.375365. hdl:10533/172862. S2CID 207551224.

[3] Shlomi Dolev; Mohammad, Ghanayim; Alexander, Binun; Sergey, Frenkel; Yeali, S. Sun (2017). "Relationship of Jaccard and edit distance in malware clustering and online identification". 16th IEEE International Symposium on Network Computing and Applications: 369–373.

[sam-4] Sam's String Metrics - Computational Linguistics and Phonetics

[5] Russell, David J., et al. "A grammar-based distance metric enables fast and accurate clustering of large sets of 16S sequences." BMC bioinformatics 11.1 (2010): 1-14.

[6] Cohen, William; Ravikumar, Pradeep; Fienberg, Stephen (2003-08-01). "A Comparison of String Distance Metrics for Name-Matching Tasks": 73–78. {{cite journal}}: Cite journal requires |journal= (help)

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v t e Strings
String metric	Approximate string matching Bitap algorithm Damerau–Levenshtein distance Edit distance Gestalt pattern matching Hamming distance Jaro–Winkler distance Lee distance Levenshtein automaton Levenshtein distance Wagner–Fischer algorithm
String-searching algorithm	Apostolico–Giancarlo algorithm Boyer–Moore string-search algorithm Boyer–Moore–Horspool algorithm Knuth–Morris–Pratt algorithm Rabin–Karp algorithm Raita algorithm Trigram search Two-way string-matching algorithm Zhu–Takaoka string matching algorithm
Multiple string searching	Aho–Corasick Commentz-Walter algorithm
Regular expression	Comparison of regular-expression engines Regular grammar Thompson's construction Nondeterministic finite automaton
Sequence alignment	BLAST Hirschberg's algorithm Needleman–Wunsch algorithm Smith–Waterman algorithm
Data structure	DAFSA Suffix array Suffix automaton Suffix tree Generalized suffix tree Rope Ternary search tree Trie
Other	Parsing Pattern matching Compressed pattern matching Longest common subsequence Longest common substring Sequential pattern mining Sorting String rewriting systems String operations

String metric

List of string metrics

Selected string measures examples

References

External links

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