Return 'similar score' based on two dictionaries' similarity in Python?

import math

ratings={'Shane': {'127 Hours': 3.0, 'Avatar': 4.0, 'Nonstop': 5.0}, 'Joe': {'127 Hours': 5.0, 'Taken 3': 4.0, 'Avatar': 5.0, 'Nonstop': 3.0}}

def cosine_similarity(vec1,vec2):
        sum11, sum12, sum22 = 0, 0, 0
        for i in range(len(vec1)):
            x = vec1[i]; y = vec2[i]
            sum11 += x*x
            sum22 += y*y
            sum12 += x*y
        return sum12/math.sqrt(sum11*sum22)

list1 = list(ratings['Shane'].values())
list2 =  list(ratings['Joe'].values())

sim = cosine_similarity(list1,list2)
print(sim)

output

o/p : 0.9205746178983233

Updated When i use :

ratings={'Shane': {'127 Hours': 5.0, 'Avatar': 4.0, 'Nonstop': 5.0},
         'Joe': {'127 Hours': 5.0, 'Taken 3': 4.0, 'Avatar': 5.0, 'Nonstop': 3.0}}

output :0.9574271077563381

Update2: Normalized length and considered keys

from math import*


ratings={'Shane': {'127 Hours': 5.0, 'Avatar': 4.0, 'Nonstop': 5.0},
         'Joe': {'127 Hours': 5.0, 'Taken 3': 4.0, 'Avatar': 5.0, 'Nonstop': 3.0},
         'Bob': {'Panic Room':5.0,'Nonstop':5.0}}


def square_rooted(x):

    return round(sqrt(sum([a*a for a in x])),3)

def cosine_similarity(x,y):

    input1 = {}
    input2 = {}
    vector2 = []
    vector1 =[]

    if len(x) > len(y):
        input1 = x
        input2 = y
    else:
        input1 = y
        input2 = x


    vector1 = list(input1.values())

    for k in input1.keys():    # Normalizing input vectors. 
        if k in input2:
            vector2.append(float(input1[k]))
        else :
            vector2.append(float(0))


    numerator = sum(a*b for a,b in zip(vector2,vector1))
    denominator = square_rooted(vector1)*square_rooted(vector2)
    return round(numerator/float(denominator),3)


print("Similarity between Shane and Joe")
print (cosine_similarity(ratings['Shane'],ratings['Joe']))

print("Similarity between Joe and Bob")
print (cosine_similarity(ratings['Joe'],ratings['Bob']))

print("Similarity between Shane and Bob")
print (cosine_similarity(ratings['Shane'],ratings['Bob']))

output:

Similarity between Shane and Joe
0.887
Similarity between Joe and Bob
0.346
Similarity between Shane and Bob
0.615

Nice explanation between jaccurd and cosine : https://datascience.stackexchange.com/questions/5121/applications-and-differences-for-jaccard-similarity-and-cosine-similarity

i am using Python 3.4

NOTE: I have assigned 0 to missing values. But you can assign some proper values too. Refer : http://www.analyticsvidhya.com/blog/2015/02/7-steps-data-exploration-preparation-building-model-part-2/

https://en.m.wikipedia.org/wiki/Jaccard_index

and now some cleaned-up sample code.

def jac(s1,s2):
    """the jaccard index between 2 sets"""
    s_union = s1.union(s2)
    s_inter = s1.intersection(s2)

    len_union = len(s_union)
    if not len_union:
        return 0

    return len(s_inter)*1.0/len_union

from itertools import permutations

ratings={'Shane': {'127 Hours': 5.0, 'Avatar': 4.0, 'Nonstop': 5.0},
     'Joe': {'127 Hours': 5.0, 'Taken 3': 4.0, 'Avatar': 5.0, 'Nonstop': 3.0},
     'Bob': {'Panic Room':5.0,'Nonstop':5.0}}

def common_movie(dict0, dict1):
    """have we rated the same movies?"""
    set0 = set(dict0.items())
    set1 = set(dict1.items())
    return jac(set0, set1)

def movies_and_ratings(dict0, dict1):
    """how do our movies and ratings line up?"""

    set_keys0 = set(dict0.keys())
    set_keys1 = set(dict1.keys())

    key_commonality = jac(set_keys0, set_keys1)

    set0 = set(dict0.items())
    set1 = set(dict1.items())

    item_commonality = jac(set0, set1)

    #ok, so now we give a proximity on key match, even if key + data dont match
    return 0.3 * key_commonality + 0.7 * item_commonality

def common_movie_ratings(dict0, dict1):
    """how do our ratings correspond on the same movies?"""

    set_keys0 = set(dict0.keys())
    set_keys1 = set(dict1.keys())

    set_common = set_keys0.intersection(set_keys1)

    set0 = set([v for k, v in dict0.items() if k in set_common])
    set1 = set([v for k, v in dict1.items() if k in set_common])

    return jac(set0, set1)

for pair in permutations(ratings.keys(), 2):

    dict0, dict1 = ratings[pair[0]], ratings[pair[1]]
    print "\n %s vs %s" % (pair)

    #make no assumption on key/value
    #order coming out of a dictionary.  So, you need to order them. 
    li = dict0.items()
    li.sort()
    print "  %s" % (li)
    li = dict1.items()
    li.sort()
    print "  %s" % (li)

    print "     common_movie    :%s" % common_movie(dict0, dict1)
    print "     movies_and_ratings:%s" % movies_and_ratings(dict0, dict1)
    print "     common_movie_ratings  :%s" % common_movie_ratings(dict0, dict1)

The output:

 Shane vs Bob
  [('127 Hours', 5.0), ('Avatar', 4.0), ('Nonstop', 5.0)]
  [('Nonstop', 5.0), ('Panic Room', 5.0)]
     common_movie    :0.25
     movies_and_ratings:0.25
     common_movie_ratings  :1.0

 Shane vs Joe
  [('127 Hours', 5.0), ('Avatar', 4.0), ('Nonstop', 5.0)]
  [('127 Hours', 5.0), ('Avatar', 5.0), ('Nonstop', 3.0), ('Taken 3', 4.0)]
     common_movie    :0.166666666667
     movies_and_ratings:0.341666666667
     common_movie_ratings  :0.333333333333

 Bob vs Shane
  [('Nonstop', 5.0), ('Panic Room', 5.0)]
  [('127 Hours', 5.0), ('Avatar', 4.0), ('Nonstop', 5.0)]
     common_movie    :0.25
     movies_and_ratings:0.25
     common_movie_ratings  :1.0

 Bob vs Joe
  [('Nonstop', 5.0), ('Panic Room', 5.0)]
  [('127 Hours', 5.0), ('Avatar', 5.0), ('Nonstop', 3.0), ('Taken 3', 4.0)]
     common_movie    :0.0
     movies_and_ratings:0.06
     common_movie_ratings  :0.0

 Joe vs Shane
  [('127 Hours', 5.0), ('Avatar', 5.0), ('Nonstop', 3.0), ('Taken 3', 4.0)]
  [('127 Hours', 5.0), ('Avatar', 4.0), ('Nonstop', 5.0)]
     common_movie    :0.166666666667
     movies_and_ratings:0.341666666667
     common_movie_ratings  :0.333333333333

 Joe vs Bob
  [('127 Hours', 5.0), ('Avatar', 5.0), ('Nonstop', 3.0), ('Taken 3', 4.0)]
  [('Nonstop', 5.0), ('Panic Room', 5.0)]
     common_movie    :0.0
     movies_and_ratings:0.06
     common_movie_ratings  :0.0