Cosine Similarity between 2 Number Lists

Question

I need to calculate the cosine similarity between two lists  let s say for example list 1 which is dataSetI and list 2 which is dataSetII  I cannot use anything such as numpy or a statistics module  I must use common modules  math  etc   and the least modules as possible  at that  to reduce time spent    Let s say dataSetI is  3  45  7  2  and dataSetII is  2  54  13  15   The length of the lists are always equal   Of course  the cosine similarity is between 0 and 1  and for the sake of it  it will be rounded to the third or fourth decimal with format round cosine  3     Thank you very much in advance for helping

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Another version  if you have a scenario where you have list of vectors and a query vector and you want to compute the cosine similarity of query vector with all the vectors in the list  you can do it in one go in the below fashion   gt  gt  gt  import numpy as np   gt  gt  gt  A        list of vectors  shape - gt  m x n array    3  45   7   2            1  23   3   4      gt  gt  gt  B        query vector  shape - gt  1 x n array   2  54  13  15     gt  gt  gt  similarity scores   A dot B    np linalg norm A  axis 1    np linalg norm B     gt  gt  gt  similarity scores array  0 97228425  0 99026919

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I did a benchmark based on several answers in the question and the following snippet is believed to be the best choice   def dot product2 v1  v2       return sum map operator mul  v1  v2     def vector cos5 v1  v2       prod   dot product2 v1  v2      len1   math sqrt dot product2 v1  v1       len2   math sqrt dot product2 v2  v2       return prod    len1   len2    The result makes me surprised that the implementation based on scipy is not the fastest one  I profiled and find that cosine in scipy takes a lot of time to cast a vector from python list to numpy array

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import math from itertools import izip  def dot product v1  v2       return sum map lambda x  x 0    x 1   izip v1  v2     def cosine measure v1  v2       prod   dot product v1  v2      len1   math sqrt dot product v1  v1       len2   math sqrt dot product v2  v2       return prod    len1   len2    You can round it after computing   cosine   format round cosine measure v1  v2   3     If you want it really short  you can use this one-liner   from math import sqrt from itertools import izip  def cosine measure v1  v2       return  lambda  x  y  z   x   sqrt y   z   reduce lambda x  y   x 0    y 0    y 1   x 1    y 0   2  x 2    y 1   2   izip v1  v2    0  0  0

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All the answers are great for situations where you cannot use NumPy  If you can  here is another approach   def cosine x  y       dot products   np dot x  y T      norm products   np linalg norm x    np linalg norm y      return dot products    norm products   EPSILON    Also bear in mind about EPSILON   1e-07 to secure the division

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You can use this simple function to calculate the cosine similarity   def cosine similarity a  b   return sum  i j for i j in zip a  b     math sqrt sum  i i for i in a     math sqrt sum  i i for i in b

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another version based on numpy only  from numpy import dot from numpy linalg import norm  cos sim   dot a  b   norm a  norm b

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Using numpy compare one list of numbers to multiple lists matrix    def cosine similarity vector matrix      return   np sum vector matrix axis 1      np sqrt np sum matrix  2 axis 1     np sqrt np sum vector  2         -1

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You can use cosine similarity function form sklearn metrics pairwise docs  In  23   from sklearn metrics pairwise import cosine similarity  In  24   cosine similarity   1  0  -1      -1 -1  0    Out 24   array   -0 5

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If you happen to be using PyTorch already  you should go with their CosineSimilarity implementation   Suppose you have two n-dimensional numpy ndarrays  v1 and v2  i e  their shapes are both  n    Here s how you get their cosine similarity   import torch import torch nn as nn  cos   nn CosineSimilarity   cos torch tensor  v1    torch tensor  v2    item     Or suppose you have two numpy ndarrays w1 and w2  whose shapes are both  m  n   The following gets you a list of cosine similarities  each being the cosine similarity between a row in w1 and the corresponding row in w2   cos torch tensor w1   torch tensor w2   tolist

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You can do this in Python using simple function   def get cosine text1  text2     vec1   text1   vec2   text2   intersection   set vec1 keys     amp  set vec2 keys      numerator   sum  vec1 x    vec2 x  for x in intersection     sum1   sum  vec1 x   2 for x in vec1 keys       sum2   sum  vec2 x   2 for x in vec2 keys       denominator   math sqrt sum1    math sqrt sum2    if not denominator       return 0 0   else       return round float numerator    denominator  3  dataSet1    3  45  7  2  dataSet2    2  54  13  15  get cosine dataSet1  dataSet2

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I don t suppose performance matters much here  but I can t resist   The zip   function completely recopies both vectors  more of a matrix transpose  actually  just to get the data in  Pythonic  order   It would be interesting to time the nuts-and-bolts implementation   import math def cosine similarity v1 v2        compute cosine similarity of v1 to v2   v1 dot v2     v1     v2         sumxx  sumxy  sumyy   0  0  0     for i in range len v1            x   v1 i   y   v2 i          sumxx    x x         sumyy    y y         sumxy    x y     return sumxy math sqrt sumxx sumyy   v1 v2    3  45  7  2    2  54  13  15  print v1  v2  cosine similarity v1 v2    Output   3  45  7  2   2  54  13  15  0 972284251712   That goes through the C-like noise of extracting elements one-at-a-time  but does no bulk array copying and gets everything important done in a single for loop  and uses a single square root   ETA  Updated print call to be a function   The original was Python 2 7  not 3 3   The current runs under Python 2 7 with a from   future   import print function statement   The output is the same  either way   CPYthon 2 7 3 on 3 0GHz Core 2 Duo    gt  gt  gt  timeit timeit  cosine similarity v1 v2   setup  from   main   import cosine similarity  v1  v2   2 4261788514654654  gt  gt  gt  timeit timeit  cosine measure v1 v2   setup  from   main   import cosine measure  v1  v2   8 794677709375264   So  the unpythonic way is about 3 6 times faster in this case

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without using any imports     math sqrt x    can be replaced with     x    5   without using numpy dot   you have to create your own dot function using list comprehension    def dot A B        return  sum a b for a b in zip A B      and then its just a simple matter of applying the cosine similarity formula   def cosine similarity a b       return dot a b       dot a a     5     dot b b      5

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You should try SciPy  It has a bunch of useful scientific routines for example   routines for computing integrals numerically  solving differential equations  optimization  and sparse matrices   It uses the superfast optimized NumPy for its number crunching  See here for installing   Note that spatial distance cosine computes the distance  and not the similarity  So  you must subtract the value from 1 to get the similarity   from scipy import spatial  dataSetI    3  45  7  2  dataSetII    2  54  13  15  result   1 - spatial distance cosine dataSetI  dataSetII

[python] Cosine Similarity between 2 Number Lists

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