A library implementing different string similarity and distance measures

# python-string-similarity

Python3.x implementation of tdebatty/java-string-similarity

A library implementing different string similarity and distance measures. A dozen of algorithms (including Levenshtein edit distance and sibblings, Jaro-Winkler, Longest Common Subsequence, cosine similarity etc.) are currently implemented. Check the summary table below for the complete list...

From pypi:

# pip install strsim # deprecated, do not use this!
pip install -U strsimpy


## Overview

The main characteristics of each implemented algorithm are presented below. The "cost" column gives an estimation of the computational cost to compute the similarity between two strings of length m and n respectively.

Normalized? Metric? Type Cost Typical usage
Levenshtein distance No Yes O(m*n) 1
Normalized Levenshtein distance
similarity
Yes No O(m*n) 1
Weighted Levenshtein distance No No O(m*n) 1 OCR
Damerau-Levenshtein 3 distance No Yes O(m*n) 1
Optimal String Alignment 3 distance No No O(m*n) 1
Jaro-Winkler similarity
distance
Yes No O(m*n) typo correction
Longest Common Subsequence distance No No O(m*n) 1,2 diff utility, GIT reconciliation
Metric Longest Common Subsequence distance Yes Yes O(m*n) 1,2
N-Gram distance Yes No O(m*n)
Q-Gram distance No No Profile O(m+n)
Cosine similarity similarity
distance
Yes No Profile O(m+n)
Jaccard index similarity
distance
Yes Yes Set O(m+n)
Sorensen-Dice coefficient similarity
distance
Yes No Set O(m+n)
Overlap coefficient similarity
distance
Yes No Set O(m+n)

[1] In this library, Levenshtein edit distance, LCS distance and their sibblings are computed using the dynamic programming method, which has a cost O(m.n). For Levenshtein distance, the algorithm is sometimes called Wagner-Fischer algorithm ("The string-to-string correction problem", 1974). The original algorithm uses a matrix of size m x n to store the Levenshtein distance between string prefixes.

If the alphabet is finite, it is possible to use the method of four russians (Arlazarov et al. "On economic construction of the transitive closure of a directed graph", 1970) to speedup computation. This was published by Masek in 1980 ("A Faster Algorithm Computing String Edit Distances"). This method splits the matrix in blocks of size t x t. Each possible block is precomputed to produce a lookup table. This lookup table can then be used to compute the string similarity (or distance) in O(nm/t). Usually, t is choosen as log(m) if m > n. The resulting computation cost is thus O(mn/log(m)). This method has not been implemented (yet).

[2] In "Length of Maximal Common Subsequences", K.S. Larsen proposed an algorithm that computes the length of LCS in time O(log(m).log(n)). But the algorithm has a memory requirement O(m.n²) and was thus not implemented here.

[3] There are two variants of Damerau-Levenshtein string distance: Damerau-Levenshtein with adjacent transpositions (also sometimes called unrestricted Damerau–Levenshtein distance) and Optimal String Alignment (also sometimes called restricted edit distance). For Optimal String Alignment, no substring can be edited more than once.

## Normalized, metric, similarity and distance

Although the topic might seem simple, a lot of different algorithms exist to measure text similarity or distance. Therefore the library defines some interfaces to categorize them.

### (Normalized) similarity and distance

• StringSimilarity : Implementing algorithms define a similarity between strings (0 means strings are completely different).
• NormalizedStringSimilarity : Implementing algorithms define a similarity between 0.0 and 1.0, like Jaro-Winkler for example.
• StringDistance : Implementing algorithms define a distance between strings (0 means strings are identical), like Levenshtein for example. The maximum distance value depends on the algorithm.
• NormalizedStringDistance : This interface extends StringDistance. For implementing classes, the computed distance value is between 0.0 and 1.0. NormalizedLevenshtein is an example of NormalizedStringDistance.

Generally, algorithms that implement NormalizedStringSimilarity also implement NormalizedStringDistance, and similarity = 1 - distance. But there are a few exceptions, like N-Gram similarity and distance (Kondrak)...

### Metric distances

The MetricStringDistance interface : A few of the distances are actually metric distances, which means that verify the triangle inequality d(x, y) <= d(x,z) + d(z,y). For example, Levenshtein is a metric distance, but NormalizedLevenshtein is not.

A lot of nearest-neighbor search algorithms and indexing structures rely on the triangle inequality.

## Shingles (n-gram) based similarity and distance

A few algorithms work by converting strings into sets of n-grams (sequences of n characters, also sometimes called k-shingles). The similarity or distance between the strings is then the similarity or distance between the sets.

Some of them, like jaccard, consider strings as sets of shingles, and don't consider the number of occurences of each shingle. Others, like cosine similarity, work using what is sometimes called the profile of the strings, which takes into account the number of occurences of each shingle.

For these algorithms, another use case is possible when dealing with large datasets:

1. compute the set or profile representation of all the strings
2. compute the similarity between sets or profiles

## Levenshtein

The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.

It is a metric string distance. This implementation uses dynamic programming (Wagner–Fischer algorithm), with only 2 rows of data. The space requirement is thus O(m) and the algorithm runs in O(m.n).

from strsimpy.levenshtein import Levenshtein

levenshtein = Levenshtein()
print(levenshtein.distance('My string', 'My $string')) print(levenshtein.distance('My string', 'My$string'))
print(levenshtein.distance('My string', 'My $string'))  ## Normalized Levenshtein This distance is computed as levenshtein distance divided by the length of the longest string. The resulting value is always in the interval [0.0 1.0] but it is not a metric anymore! The similarity is computed as 1 - normalized distance. from strsimpy.normalized_levenshtein import NormalizedLevenshtein normalized_levenshtein = NormalizedLevenshtein() print(normalized_levenshtein.distance('My string', 'My$string'))
print(normalized_levenshtein.distance('My string', 'My $string')) print(normalized_levenshtein.distance('My string', 'My$string'))

print(normalized_levenshtein.similarity('My string', 'My $string')) print(normalized_levenshtein.similarity('My string', 'My$string'))
print(normalized_levenshtein.similarity('My string', 'My \$string'))


## Weighted Levenshtein

An implementation of Levenshtein that allows to define different weights for different character substitutions.

This algorithm is usually used for optical character recognition (OCR) applications. For OCR, the cost of substituting P and R is lower then the cost of substituting P and M for example because because from and OCR point of view P is similar to R.

It can also be used for keyboard typing auto-correction. Here the cost of substituting E and R is lower for example because these are located next to each other on an AZERTY or QWERTY keyboard. Hence the probability that the user mistyped the characters is higher.

from strsimpy.weighted_levenshtein import WeightedLevenshtein

def insertion_cost(char):
return 1.0

def deletion_cost(char):
return 1.0

def substitution_cost(char_a, char_b):
if char_a == 't' and char_b == 'r':
return 0.5
return 1.0

weighted_levenshtein = WeightedLevenshtein(
substitution_cost_fn=substitution_cost,
insertion_cost_fn=insertion_cost,
deletion_cost_fn=deletion_cost)
print(weighted_levenshtein.distance('String1', 'String2'))


## Damerau-Levenshtein

Similar to Levenshtein, Damerau-Levenshtein distance with transposition (also sometimes calls unrestricted Damerau-Levenshtein distance) is the minimum number of operations needed to transform one string into the other, where an operation is defined as an insertion, deletion, or substitution of a single character, or a transposition of two adjacent characters.

It does respect triangle inequality, and is thus a metric distance.

This is not to be confused with the optimal string alignment distance, which is an extension where no substring can be edited more than once.

from strsimpy.damerau import Damerau

damerau = Damerau()
print(damerau.distance('ABCDEF', 'ABDCEF'))
print(damerau.distance('ABCDEF', 'BACDFE'))
print(damerau.distance('ABCDEF', 'ABCDE'))
print(damerau.distance('ABCDEF', 'BCDEF'))
print(damerau.distance('ABCDEF', 'ABCGDEF'))
print(damerau.distance('ABCDEF', 'POIU'))


Will produce:

1.0
2.0
1.0
1.0
1.0
6.0


## Optimal String Alignment

The Optimal String Alignment variant of Damerau–Levenshtein (sometimes called the restricted edit distance) computes the number of edit operations needed to make the strings equal under the condition that no substring is edited more than once, whereas the true Damerau–Levenshtein presents no such restriction. The difference from the algorithm for Levenshtein distance is the addition of one recurrence for the transposition operations.

Note that for the optimal string alignment distance, the triangle inequality does not hold and so it is not a true metric.

from strsimpy.optimal_string_alignment import OptimalStringAlignment

optimal_string_alignment = OptimalStringAlignment()
print(optimal_string_alignment.distance('CA', 'ABC'))


Will produce:

3.0


## Jaro-Winkler

Jaro-Winkler is a string edit distance that was developed in the area of record linkage (duplicate detection) (Winkler, 1990). The Jaro–Winkler distance metric is designed and best suited for short strings such as person names, and to detect typos.

Jaro-Winkler computes the similarity between 2 strings, and the returned value lies in the interval [0.0, 1.0]. It is (roughly) a variation of Damerau-Levenshtein, where the substitution of 2 close characters is considered less important then the substitution of 2 characters that a far from each other.

The distance is computed as 1 - Jaro-Winkler similarity.

from strsimpy.jaro_winkler import JaroWinkler

jarowinkler = JaroWinkler()
print(jarowinkler.similarity('My string', 'My tsring'))
print(jarowinkler.similarity('My string', 'My ntrisg'))


will produce:

0.9740740740740741
0.8962962962962963


## Longest Common Subsequence

The longest common subsequence (LCS) problem consists in finding the longest subsequence common to two (or more) sequences. It differs from problems of finding common substrings: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences.

It is used by the diff utility, by Git for reconciling multiple changes, etc.

The LCS distance between strings X (of length n) and Y (of length m) is n + m - 2 |LCS(X, Y)| min = 0 max = n + m

LCS distance is equivalent to Levenshtein distance when only insertion and deletion is allowed (no substitution), or when the cost of the substitution is the double of the cost of an insertion or deletion.

This class implements the dynamic programming approach, which has a space requirement O(m.n), and computation cost O(m.n).

In "Length of Maximal Common Subsequences", K.S. Larsen proposed an algorithm that computes the length of LCS in time O(log(m).log(n)). But the algorithm has a memory requirement O(m.n²) and was thus not implemented here.

from strsimpy.longest_common_subsequence import LongestCommonSubsequence
lcs = LongestCommonSubsequence()
print(lcs.distance('AGCAT', 'GAC'))
4
print(lcs.length('AGCAT', 'GAC'))
2
print(lcs.distance('AGCAT', 'AGCT'))
1
print(lcs.length('AGCAT', 'AGCT'))
4


## Metric Longest Common Subsequence

Distance metric based on Longest Common Subsequence, from the notes "An LCS-based string metric" by Daniel Bakkelund. http://heim.ifi.uio.no/~danielry/StringMetric.pdf

The distance is computed as 1 - |LCS(s1, s2)| / max(|s1|, |s2|)

from strsimpy.metric_lcs import MetricLCS

metric_lcs = MetricLCS()
s1 = 'ABCDEFG'
s2 = 'ABCDEFHJKL'

# LCS: ABCDEF => length = 6
# longest = s2 => length = 10
# => 1 - 6/10 = 0.4
print(metric_lcs.distance(s1, s2))

# LCS: ABDF => length = 4
# longest = ABDEF => length = 5
# => 1 - 4 / 5 = 0.2
print(metric_lcs.distance('ABDEF', 'ABDIF'))


will produce:

0.4
0.19999999999999996


## N-Gram

Normalized N-Gram distance as defined by Kondrak, "N-Gram Similarity and Distance", String Processing and Information Retrieval, Lecture Notes in Computer Science Volume 3772, 2005, pp 115-126.

http://webdocs.cs.ualberta.ca/~kondrak/papers/spire05.pdf

The algorithm uses affixing with special character '\n' to increase the weight of first characters. The normalization is achieved by dividing the total similarity score the original length of the longest word.

In the paper, Kondrak also defines a similarity measure, which is not implemented (yet).

from strsimpy.ngram import NGram

twogram = NGram(2)
print(twogram.distance('ABCD', 'ABTUIO'))

s1 = 'Adobe CreativeSuite 5 Master Collection from cheap 4zp'
s2 = 'Adobe CreativeSuite 5 Master Collection from cheap d1x'
fourgram = NGram(4)
print(fourgram.distance(s1, s2))


## Shingle (n-gram) based algorithms

A few algorithms work by converting strings into sets of n-grams (sequences of n characters, also sometimes called k-shingles). The similarity or distance between the strings is then the similarity or distance between the sets.

The cost for computing these similarities and distances is mainly domnitated by k-shingling (converting the strings into sequences of k characters). Therefore there are typically two use cases for these algorithms:

Directly compute the distance between strings:

from strsimpy.qgram import QGram

qgram = QGram(2)
print(qgram.distance('ABCD', 'ABCE'))


Or, for large datasets, pre-compute the profile of all strings. The similarity can then be computed between profiles:

from strsimpy.cosine import Cosine

cosine = Cosine(2)
s0 = 'My first string'
s1 = 'My other string...'
p0 = cosine.get_profile(s0)
p1 = cosine.get_profile(s1)
print(cosine.similarity_profiles(p0, p1))


Pay attention, this only works if the same KShingling object is used to parse all input strings !

### Q-Gram

Q-gram distance, as defined by Ukkonen in "Approximate string-matching with q-grams and maximal matches" http://www.sciencedirect.com/science/article/pii/0304397592901434

The distance between two strings is defined as the L1 norm of the difference of their profiles (the number of occurences of each n-gram): SUM( |V1_i - V2_i| ). Q-gram distance is a lower bound on Levenshtein distance, but can be computed in O(m + n), where Levenshtein requires O(m.n)

### Cosine similarity

The similarity between the two strings is the cosine of the angle between these two vectors representation, and is computed as V1 . V2 / (|V1| * |V2|)

Distance is computed as 1 - cosine similarity.

### Jaccard index

Like Q-Gram distance, the input strings are first converted into sets of n-grams (sequences of n characters, also called k-shingles), but this time the cardinality of each n-gram is not taken into account. Each input string is simply a set of n-grams. The Jaccard index is then computed as |V1 inter V2| / |V1 union V2|.

Distance is computed as 1 - similarity. Jaccard index is a metric distance.

### Sorensen-Dice coefficient

Similar to Jaccard index, but this time the similarity is computed as 2 * |V1 inter V2| / (|V1| + |V2|).

Distance is computed as 1 - similarity.

### Overlap coefficient (i.e., Szymkiewicz-Simpson)

Very similar to Jaccard and Sorensen-Dice measures, but this time the similarity is computed as |V1 inter V2| / Min(|V1|,|V2|). Tends to yield higher similarity scores compared to the other overlapping coefficients. Always returns the highest similarity score (1) if one given string is the subset of the other.

Distance is computed as 1 - similarity.

## Experimental

### SIFT4

SIFT4 is a general purpose string distance algorithm inspired by JaroWinkler and Longest Common Subsequence. It was developed to produce a distance measure that matches as close as possible to the human perception of string distance. Hence it takes into account elements like character substitution, character distance, longest common subsequence etc. It was developed using experimental testing, and without theoretical background.

from strsimpy import SIFT4

s = SIFT4()

# result: 11.0
s.distance('This is the first string', 'And this is another string') # 11.0
# result: 12.0
s.distance('Lorem ipsum dolor sit amet, consectetur adipiscing elit.', 'Amet Lorm ispum dolor sit amet, consetetur adixxxpiscing elit.', maxoffset=10)


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