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A package for string distance and similarity metrics

Project description


Python library for distance and similarity metrics


From pypi:

pip install hermetrics


Hermetrics is a library designed for use in experimentation with string metrics. The library features a base class Metric which is highly configurable and can be used to implement custom metrics.

Based on Metric are some common string metrics already implemented to compute the distance between two strings. Some common edit distance metrics such as Levenshtein can be parametrized with different costs for each edit operation, althought have been only thorougly tested with costs equal to 1. Also, the implemented metrics can be used to compare any iterable in addition to strings, but more tests are needed.

A metric has three main methods distance, normalized_distance and similarity. In general the distance method computes the absolute distance between two strings, whereas normalized_distance can be used to scale the distance to a particular range, usually (0,1), and the similarity method being normally defined as (1-normalized_distance).

The normalization of the distance can be customized overriding the auxiliary methods for its computation. Those methods are max_distance, min_distance and normalize.

Metric class

Metric is a base class that can receive as arguments six specific functions to be used as methods for the metric being implemented. The class constructor just assign the functions received as parameters to the class methods. If ypu omit some parameter then a default method is used, which allows you to implement metrics without the need to rewrite some of the functionality that is common among metrics.

class Metric:
    """Class for metric implementations"""

    def __init__(self, distance=None, max_distance=None, min_distance=None, normalize=None, normalized_distance=None,  similarity=None, name='Generic'):
        """Class constructor - receives a function for distance or similarity evaluation""" = name
        self.distance = distance or self.distance
        self.max_distance = max_distance or self.max_distance
        self.min_distance = min_distance or self.min_distance
        self.normalize = normalize or self.normalize        
        self.normalized_distance = normalized_distance or self.normalized_distance
        self.similarity = similarity or self.similarity

Default methods

Description of default methods for the Metric class.

In general a method of a metric receives three parameters:

  • source. The source string or iterable to compare.
  • target. The target string or iterable to compare.
  • cost=1. If a number, the unit cost for any edit operations. If a tuple, the cost for edit operations in the following order (deletion, insertion, substitution, transposition).


The distance method computes the total cost of transforming the source string on the target string. The default method just return 0 if the strings are equal and 1 otherwise.


Returns the maximum value of the distance between source and target given a specific cost for edit operations. The default method just return 1 given source and target don't have both length=0, in that case just return 0.


Return 0.


This method is used to scale a value between two limits, usually those obtained by max_distance and min_distance, to the (0,1) range. Unlike the other methods, normalize doesn't receive the usual arguments (source, target and cost), instead receive the following:

  • x. The value to be normalized.
  • low=0. The minimum value for the normalization, usually obtained with min_distance method.
  • high=1. The maximum value for the normalization, usually obtained with max_distance method.

normalized distance

Scale the distance between source and target for specific cost to the (0,1) range using max_distance, min_distance and normalize.


Computes how similar are source and target given a specific cost. By default defined as 1 - normalized_distance so the result is also in the (0,1) range.


For the time being the following metrics have been implemented:


The Hamming distance count the positions where two strings differ. Normally the Hamming distance is only defined for strings of equal size but in this implementation strings of different size can be compared counting the difference in size as part of the distance.

from hermetrics.hamming import Hamming

ham = Hamming()

ham.distance('abcd', 'abce') # 1
ham.normalized_distance('abcd', 'abce') # 0.25
ham.similarity('abcd', 'abce') # 0.75


Levenshtein distance is usually known as "the" edit distance. It is defined as the minimum number of edit operations (deletion, insertion and substitution) to transform the source string into the target string. The algorithm for distance computation is implemented using the dynamic programming approach with the full matrix construction, althought there are optimizations for time and space complexity those are not implemented here.

from hermetrics.levenshtein import Levenshtein

lev = Levenshtein()

lev.distance('ace', 'abcde') # 2
lev.normalized_distance('ace', 'abcde') # 0.4
lev.similarity('ace', 'abcde') # 0.6

# With cost=2
lev.distance('ace', 'abcde', 2) # 4
lev.normalized_distance('ace', 'abcde', 2) # 0.4
lev.similarity('ace', 'abcde', 2) # 0.6

# With different costs for deletion, insertion and substituion
lev.distance('ace', 'abcde', (1, 1.25, 1.5)) # 2.5
lev.normalized_distance('ace', 'abcde', (1, 1.25, 1.5)) # 0.3571
lev.similarity('ace', 'abcde', (1, 1.25, 1.5)) # 0.6429

OSA (Optimal String Alignment)

The OSA distance is based on the Levenshtein distance but counting the transposition as a valid edit operation with the restriction that no substring can be transposed more than once.

from hermetrics.osa import Osa

osa = Osa()

osa.distance('abcd', 'abdc') # 1
osa.normalized_distance('abcd', 'abdc') # 0.25
osa.similarity('abcd', 'abdc') # 0.75

# With different costs for deletion, insertion, substituion and transposition
osa.distance('ace', 'abcde', (0.75, 1, 1.25, 1.5)) # 2
osa.normalized_distance('ace', 'abcde',  (0.75, 1, 1.25, 1.5)) # 0.3478
osa.similarity('ace', 'abcde',  (0.75, 1, 1.25, 1.5)) # 0.6522


The Damerau-Levenshtein distance is like OSA but without the restriction on the number of transpositions for the same substring.

from hermetrics.damerau_levenshtein import DamerauLevenshtein

dam = DamerauLevenshtein()

dam.distance('abcd', 'cbad') # 2
dam.normalized_distance('abcd', 'cbad') # 0.5
dam.similarity('abcd', 'cbad') # 0.5

# With different costs for deletion, insertion, substituion and transposition
dam.distance('ace', 'abcde', (0.75, 1, 1.25, 1.5)) # 2
dam.normalized_distance('ace', 'abcde',  (0.75, 1, 1.25, 1.5)) # 0.3478
dam.similarity('ace', 'abcde', (0.75, 1, 1.25, 1.5)) # 0.6522


The Jaccard index considers the strings as a bag-of-characters set and computes the cardinality of the intersection over the cardinality of the union. The distance function for Jaccard index is already normalized.

from hermetrics.jaccard import Jaccard

jac = Jaccard()

jac.distance('abcd', 'abce') # 0.4 
jac.similarity('abcd', 'abce') # 0.6

Dice (Sorenson-Dice)

Is related to Jaccard index in the following manner:

from hermetrics.dice import Dice

dic = Dice()

dic.distance('abcd', 'abce') # 0.25
dic.similarity('abcd', 'abce') # 0.75


Jaro distance is based on the matching characters present on two strings and the number of transpositions between them. A matching occurs when a character of a string is present on the other string but in a position no further away that certain threshold based on the lenght of the strings. The Jaro distance is normalized.

from hermetrics.jaro import Jaro

jar = Jaro()

jar.distance('abcd', 'abe') # 0.278
jar.similarity('abcd', 'abe') # 0.722


Extension of Jaro distance with emphasis on the first characters of the strings, so strings that have matching characters on the beginning have more similarity than those that have matching characters at the end. This metric depends on an additional parameter p (with 0<=p<=0.25 and default p=0.1) that is a weighting factor for additional score obtained for matching characters at the beginning of the strings..

from hermetrics.jaro_winkler import JaroWinkler

jaw = JaroWinkler()

jaw.distance('abcd', 'abe') # 0.222
jaw.similarity('abcd', 'abe') # 0.778

jaw.similarity('abcd', 'abe', p=0.05) # 0.750
jaw.similarity('abcd', 'abe', p=0.15) # 0.806
jaw.similarity('abcd', 'abe', p=0.25) # 0.861

To Do

  • Use **kwargs instead of cost tuples
  • Weighted Levenshtein
  • Show matrix for Levenshtein like distances
  • Allow variable maximun prefix length in Jaro-Winkler
  • Implement backtracking of operations
  • More metrics
  • Type hints?

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