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.

Answer 1

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:

>>> timeit.timeit("cosine_similarity(v1,v2)",setup="from __main__ import cosine_similarity, v1, v2")
2.4261788514654654
>>> 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.

Answer 2

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]])

Answer 3

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()

Answer 4

You can do this in Python using simple function:

def get_cosine(text1, text2):
  vec1 = text1
  vec2 = text2
  intersection = set(vec1.keys()) & 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)

Answer 5

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]