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Kotlin String Similarity

Kotlin String Similarity is a port of tdebatty's java-string-similarity to Kotlin Multiplatform.

Kotlin String Similarity implements various string similarity and distance measures. It contains over a dozen such algorithms, including Levenshtein distance (and siblings), Jaro-Winkler, Longest Common Subsequence, cosine similarity, and many others. Check the summary table below for the complete list.

PRs to add more are always welcome.

Including

You can include Kotlin String Similarity in your project by adding the following, depending on your platform:

Maven

<dependency>
    <groupId>ca.solo-studios</groupId>
    <artifactId>kt-string-similarity</artifactId>
    <version>VERSION</version>
</dependency>

Gradle Groovy

implementation 'ca.solo-studios:kt-string-similarity:VERSION'

Gradle Kotlin

implementation("ca.solo-studios:kt-string-similarity:VERSION")

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.

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

[1] In this library, Levenshtein edit distance, LCS distance and their sibblings are computed using the dynamic programming method, which has a cost $O(m \times n)$. 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 $t \times t$. 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 $O(\frac{nm}{t})$. Usually, $t$ is chosen as $log(m)$ if $m &gt; n$. The resulting computation cost is thus $O(\frac{mn}{log(m)})$. 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 $O(log(m) \times log(n))$. But the algorithm has a memory requirement $O(m \times n^2)$ 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.

Algorithms

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: The interface extends StringSimilarity. Implementing algorithms compute a similarity that has been normalized based on the number of operations performed. This means that for non-weighted implementations, the result will always be between 0 and 1. Jaro-Winkler is an example of this.
  • 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. Implementing algorithms compute a distance that has been normalized based on the number of operations performed. This means that for non-weighted implementations, the result will always be between 0 and 1. NormalizedLevenshtein is an example of this.

Generally, algorithms that implement NormalizedStringSimilarity also implement NormalizedStringDistance, and similarity = 1 - distance. ( !! Only if the result is always between 0 and 1.)
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 $d(x, y) &lt;= d(x,z) + d(z,y)$`. 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. You can check "Similarity Search, The Metric Space Approach" by Zezula et al. for a survey. These cannot be used with non metric similarity measures.

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 $O(m \times n)$.

fun main() {
    val levenshtein = Levenshtein()

    println(levenshtein.distance("My string", "My \$tring")) // prints 1.0
}

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.

fun main() {
    val normLevenshtein = NormalizedLevenshtein()

    println(normLevenshtein.distance("My string", "My \$tring")) // prints 0.1111111111111111
}

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 T 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.

fun main() {
    val weightedLevenshtein = WeightedLevenshtein({ old, new ->
        if (old == 't' && new == 'r') 0.5 else 1.0
    })

    println(weightedLevenshtein.distance("String1", "Srring2")) // prints 1.5
}

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.

fun main() {
    val damerau = Damerau()
    
    println(damerau.distance("ABCDEF", "ABDCEF")) // prints 1.0
    
    // 2 substitutions
    println(d.distance("ABCDEF", "BACDFE")) // prints 2.0
    
    // 1 deletion
    println(d.distance("ABCDEF", "ABCDE")) // prints 1.0
    println(d.distance("ABCDEF", "BCDEF")) // prints 1.0
    println(d.distance("ABCDEF", "ABCGDEF")) // prints 1.0
    
    // All different
    println(d.distance("ABCDEF", "POIU")) // prints 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.

fun main() {
    val optimalStringAlignment = OptimalStringAlignment()
    
    println(optimalStringAlignment.distance("CA", "ABC")) // prints 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 transposition 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 transposition of 2 close characters is considered less important than the transposition of 2 characters that are far from each other. Jaro-Winkler penalizes additions or substitutions that cannot be expressed as transpositions.

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

fun main() {
    val jaroWinkler = JaroWinkler()
    
    // substitution of s and t
    println(jaroWinkler.similarity("My string", "My tsring")) // prints 0.9740740656852722
    
    // substitution of s and n
    println(jaroWinkler.similarity("My string", "My ntrisg")) // prints 0.8962963223457336
}

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 $n + m - 2 |LCS(X, Y)|$ $\text{min} = 0$ $\text{max} = n + m$

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 $O(m \times n)$, and computation cost $O(m \times n)$.

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

fun main() {
    val longestCommonSubsequence = LongestCommonSubsequence()
    
    println(longestCommonSubsequence.distance("AGCAT", "GAC")) // prints 4.0
    
    println(longestCommonSubsequence.distance("AGCAT", "AGCT")) // prints 1.0
}

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|)

fun main() {
    val metricLCS = MetricLCS()
    
    // LCS: "ABCDEF" => length = 6
    // longest = "ABCDEFHJKL" => length = 10
    // => 1 - 6/10 = 0.4
    println(metricLCS.distance("ABCDEFG", "ABCDEFHJKL"))
    
    // LCS: "ABDF" => length = 4
    // longest = "ABDEF" => length = 5
    // => 1 - 4 / 5 = 0.2
    println(metricLCS.distance("ABDEF", "ABDIF"))
}

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).

fun main() {
    val twogram = NGram(2)
    println(twogram.distance("ABCD", "ABTUIO")) // prints 0.583333
    
    val s1 = "Adobe CreativeSuite 5 Master Collection from cheap 4zp"
    val s2 = "Adobe CreativeSuite 5 Master Collection from cheap d1x"
    val ngram = NGram(4)
    println(ngram.distance(s1, s2)) // prints 0.97222
}

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:

fun main() {
    val dig = QGram(2)
    
    // AB BC CD CE
    // 1  1  1  0
    // 1  1  0  1
    // Total: 2
    
    println(dig.distance("ABCD", "ABCE")) // prints 2
}

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

/**
 * Example of computing cosine similarity with pre-computed profiles.
 */
fun main() {
    val s1 = "My first string"
    val s2 = "My other string..."
    
    // Let's work with sequences of 2 characters...
    Cosine cosine = new Cosine(2)
    
    // Pre-compute the profile of strings
    val profile1 = cosine.profile(s1)
    val profile2 = cosine.profile(s2)
    
    println(cosine.similarity(profile1, profile2)) // prints 0.516185
}

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 $O(m \times n)$

Cosine similarity

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

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 $|V1 \cap V2| / |V1 \cup V2|$.

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 $2 * |V1 \cap V2| / (|V1| + |V2|)$.

Distance is computed as 1 - similarity.

Ratcliff-Obershelp

Ratcliff/Obershelp Pattern Recognition, also known as Gestalt Pattern Matching, is a string-matching algorithm for determining the similarity of two strings. It was developed in 1983 by John W. Ratcliff and John A. Obershelp and published in the Dr. Dobb's Journal in July 1988

Ratcliff/Obershelp computes the similarity between 2 strings, and the returned value lies in the interval $[0.0, 1.0]$.

The distance is computed as 1 - Ratcliff/Obershelp similarity.

fun main() {
    val ratcliffObershelp = RatcliffObershelp()
    
    // substitution of s and t
    println(ratcliffObershelp.similarity("My string", "My tsring")) // prints 0.8888888888888888
    
    // substitution of s and n
    println(ratcliffObershelp.similarity("My string", "My ntrisg")) // prints 0.7777777777777778
}

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.

fun main() {
    val s1 = "This is the first string"
    val s2 = "And this is another string"
    val sift4 = Sift4(maxOffset = 5)
    
    val expectedResult = 11.0
    val result = sift4.distance(s1, s2)
    
    assertEquals(expectedResult, result, 0.0)
}

Users

Use java-string-similarity in your project and want it to be mentioned here? Don't hesitate to drop me a line!