# Find the similarity metric between two strings

## Question:

How do I get the probability of a string being similar to another string in Python?

I want to get a decimal value like 0.9 (meaning 90%) etc. Preferably with standard Python and library.

e.g.

``````similar("Apple","Appel") #would have a high prob.

similar("Apple","Mango") #would have a lower prob.
``````

You can create a function like:

``````def similar(w1, w2):
w1 = w1 + ' ' * (len(w2) - len(w1))
w2 = w2 + ' ' * (len(w1) - len(w2))
return sum(1 if i == j else 0 for i, j in zip(w1, w2)) / float(len(w1))
``````

There is a built in.

``````from difflib import SequenceMatcher

def similar(a, b):
return SequenceMatcher(None, a, b).ratio()
``````

Using it:

``````>>> similar("Apple","Appel")
0.8
>>> similar("Apple","Mango")
0.0
``````

I think maybe you are looking for an algorithm describing the distance between strings. Here are some you may refer to:

`TheFuzz` is a package that implements Levenshtein distance in python, with some helper functions to help in certain situations where you may want two distinct strings to be considered identical. For example:

``````>>> fuzz.ratio("fuzzy wuzzy was a bear", "wuzzy fuzzy was a bear")
91
>>> fuzz.token_sort_ratio("fuzzy wuzzy was a bear", "wuzzy fuzzy was a bear")
100
``````

Package distance includes Levenshtein distance:

``````import distance
distance.levenshtein("lenvestein", "levenshtein")
# 3
``````

# Solution #1: Python builtin

use SequenceMatcher from difflib

pros:
native python library, no need extra package.
cons: too limited, there are so many other good algorithms for string similarity out there.

example :

``````>>> from difflib import SequenceMatcher
>>> s = SequenceMatcher(None, "abcd", "bcde")
>>> s.ratio()
0.75
``````

# Solution #2: jellyfish library

its a very good library with good coverage and few issues.
it supports:
– Levenshtein Distance
– Damerau-Levenshtein Distance
– Jaro Distance
– Jaro-Winkler Distance
– Match Rating Approach Comparison
– Hamming Distance

pros:
easy to use, gamut of supported algorithms, tested.
cons: not native library.

example:

``````>>> import jellyfish
>>> jellyfish.levenshtein_distance(u'jellyfish', u'smellyfish')
2
>>> jellyfish.jaro_distance(u'jellyfish', u'smellyfish')
0.89629629629629637
>>> jellyfish.damerau_levenshtein_distance(u'jellyfish', u'jellyfihs')
1
``````

The builtin `SequenceMatcher` is very slow on large input, here’s how it can be done with diff-match-patch:

``````from diff_match_patch import diff_match_patch

def compute_similarity_and_diff(text1, text2):
dmp = diff_match_patch()
dmp.Diff_Timeout = 0.0
diff = dmp.diff_main(text1, text2, False)

# similarity
common_text = sum([len(txt) for op, txt in diff if op == 0])
text_length = max(len(text1), len(text2))
sim = common_text / text_length

return sim, diff
``````

Note, `difflib.SequenceMatcher` only finds the longest contiguous matching subsequence, this is often not what is desired, for example:

``````>>> a1 = "Apple"
>>> a2 = "Appel"
>>> a1 *= 50
>>> a2 *= 50
>>> SequenceMatcher(None, a1, a2).ratio()
0.012  # very low
>>> SequenceMatcher(None, a1, a2).get_matching_blocks()
[Match(a=0, b=0, size=3), Match(a=250, b=250, size=0)]  # only the first block is recorded
``````

Finding the similarity between two strings is closely related to the concept of pairwise sequence alignment in bioinformatics. There are many dedicated libraries for this including biopython. This example implements the Needleman Wunsch algorithm:

``````>>> from Bio.Align import PairwiseAligner
>>> aligner = PairwiseAligner()
>>> aligner.score(a1, a2)
200.0
>>> aligner.algorithm
'Needleman-Wunsch'
``````

Using biopython or another bioinformatics package is more flexible than any part of the python standard library since many different scoring schemes and algorithms are available. Also, you can actually get the matching sequences to visualise what is happening:

``````>>> alignment = next(aligner.align(a1, a2))
>>> alignment.score
200.0
>>> print(alignment)
Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-Apple-
|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-|||-|-
App-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-elApp-el
``````

You can find most of the text similarity methods and how they are calculated under this link: https://github.com/luozhouyang/python-string-similarity#python-string-similarity
Here some examples;

• Normalized, metric, similarity and distance

• (Normalized) similarity and distance

• Metric distances

• Shingles (n-gram) based similarity and distance
• Levenshtein
• Normalized Levenshtein
• Weighted Levenshtein
• Damerau-Levenshtein
• Optimal String Alignment
• Jaro-Winkler
• Longest Common Subsequence
• Metric Longest Common Subsequence
• N-Gram
• Shingle(n-gram) based algorithms
• Q-Gram
• Cosine similarity
• Jaccard index
• Sorensen-Dice coefficient
• Overlap coefficient (i.e.,Szymkiewicz-Simpson)

There are many metrics to define similarity and distance between strings as mentioned above. I will give my 5 cents by showing an example of `Jaccard similarity` with `Q-Grams` and an example with `edit distance`.

The libraries

``````from nltk.metrics.distance import jaccard_distance
from nltk.util import ngrams
from nltk.metrics.distance  import edit_distance
``````

Jaccard Similarity

``````1-jaccard_distance(set(ngrams('Apple', 2)), set(ngrams('Appel', 2)))
``````

and we get:

``````0.33333333333333337
``````

And for the `Apple` and `Mango`

``````1-jaccard_distance(set(ngrams('Apple', 2)), set(ngrams('Mango', 2)))
``````

and we get:

``````0.0
``````

Edit Distance

``````edit_distance('Apple', 'Appel')
``````

and we get:

``````2
``````

And finally,

``````edit_distance('Apple', 'Mango')
``````

and we get:

``````5
``````

Cosine Similarity on Q-Grams (q=2)

Another solution is to work with the `textdistance` library. I will provide an example of `Cosine Similarity`

``````import textdistance
1-textdistance.Cosine(qval=2).distance('Apple', 'Appel')
``````

and we get:

``````0.5
``````

Textdistance:

TextDistance – python library for comparing distance between two or more sequences by many algorithms. It has Textdistance

• 30+ algorithms
• Pure python implementation
• Simple usage
• More than two sequences comparing
• Some algorithms have more than one implementation in one class.
• Optional numpy usage for maximum speed.

Example1:

``````import textdistance
textdistance.hamming('test', 'text')
``````

Output:

1

Example2:

``````import textdistance

textdistance.hamming.normalized_similarity('test', 'text')
``````

Output:

0.75

Thanks and Cheers!!!

Here’s what i thought of:

``````import string

def match(a,b):
a,b = a.lower(), b.lower()
error = 0
for i in string.ascii_lowercase:
error += abs(a.count(i) - b.count(i))
total = len(a) + len(b)
return (total-error)/total

if __name__ == "__main__":
print(match("pple inc", "Apple Inc."))
``````

BLEUscore

BLEU, or the Bilingual Evaluation Understudy, is a score for comparing
a candidate translation of text to one or more reference translations.

A perfect match results in a score of 1.0, whereas a perfect mismatch
results in a score of 0.0.

Although developed for translation, it can be used to evaluate text
generated for a suite of natural language processing tasks.

Code:

``````import nltk
from nltk.translate import bleu
from nltk.translate.bleu_score import SmoothingFunction
smoothie = SmoothingFunction().method4

C1='Text'
C2='Best'

print('BLEUscore:',bleu([C1], C2, smoothing_function=smoothie))
``````

Examples: By updating C1 and C2.

``````C1='Test' C2='Test'

BLEUscore: 1.0

C1='Test' C2='Best'

BLEUscore: 0.2326589746035907

C1='Test' C2='Text'

BLEUscore: 0.2866227639866161
``````

You can also compare sentence similarity:

``````C1='It is tough.' C2='It is rough.'

BLEUscore: 0.7348889200874658

C1='It is tough.' C2='It is tough.'

BLEUscore: 1.0
``````

• ### Works Well in most scenarios

In stack overflow, when you tries to add a tag or post a question, it bring up all relevant stuff. This is so convenient and is exactly the algorithm that I am looking for. Therefore, I coded a query set similarity filter.

``````def compare(qs, ip):
al = 2
v = 0
for ii, letter in enumerate(ip):
if letter == qs[ii]:
v += al
else:
ac = 0
for jj in range(al):
if ii - jj < 0 or ii + jj > len(qs) - 1:
break
elif letter == qs[ii - jj] or letter == qs[ii + jj]:
ac += jj
break
v += ac
return v

def getSimilarQuerySet(queryset, inp, length):
return [k for tt, (k, v) in enumerate(reversed(sorted({it: compare(it, inp) for it in queryset}.items(), key=lambda item: item)))][:length]

if __name__ == "__main__":
print(compare('apple', 'mongo'))
# 0
print(compare('apple', 'apple'))
# 10
print(compare('apple', 'appel'))
# 7
print(compare('dude', 'ud'))
# 1
print(compare('dude', 'du'))
# 4
print(compare('dude', 'dud'))
# 6

print(compare('apple', 'mongo'))
# 2
print(compare('apple', 'appel'))
# 8

print(getSimilarQuerySet(
[
"java",
"jquery",
"javascript",
"jude",
"aja",
],
"ja",
2,
))
# ['javascript', 'java']
``````

### Explanation

• `compare` takes two string and returns a positive integer.
• you can edit the `al` allowed variable in `compare`, it indicates how large the range we need to search through. It works like this: two strings are iterated, if same character is find at same index, then accumulator will be added to a largest value. Then, we search in the index range of `allowed`, if matched, add to the accumulator based on how far the letter is. (the further, the smaller)
• `length` indicate how many items you want as result, that is most similar to input string.

Adding the Spacy NLP library also to the mix;

``````@profile
def main():
str1= "Mar 31 09:08:41  The world is beautiful"
str2= "Mar 31 19:08:42  Beautiful is the world"
print("NLP Similarity=",nlp(str1).similarity(nlp(str2)))
print("Diff lib similarity",SequenceMatcher(None, str1, str2).ratio())
print("Jellyfish lib similarity",jellyfish.jaro_distance(str1, str2))

if __name__ == '__main__':

main()
``````

Run with Robert Kern’s line_profiler

``````kernprof -l -v ./python/loganalysis/testspacy.py

NLP Similarity= 0.9999999821467294
Diff lib similarity 0.5897435897435898
Jellyfish lib similarity 0.8561253561253562
``````

However the time’s are revealing

``````Function: main at line 32

Line #      Hits         Time  Per Hit   % Time  Line Contents
==============================================================
32                                           @profile
33                                           def main():
34         1          1.0      1.0      0.0      str1= "Mar 31 09:08:41  The world is beautiful"
35         1          0.0      0.0      0.0      str2= "Mar 31 19:08:42  Beautiful is the world"
36         1      43248.0  43248.0     99.1      print("NLP Similarity=",nlp(str1).similarity(nlp(str2)))
37         1        375.0    375.0      0.9      print("Diff lib similarity",SequenceMatcher(None, str1, str2).ratio())
38         1         30.0     30.0      0.1      print("Jellyfish lib similarity",jellyfish.jaro_distance(str1, str2))
``````
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