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similarity.py
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similarity.py
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from __future__ import division
from math import sqrt
def sim_distance(prefs, item1, item2):
#get the list of shared items
si = {};
for item in prefs[item1]:
if item in prefs[item2]:
si[item] = 1;
#if they have no shared items,return 0;
if len(si) == 0: return 0;
#Add the squares of all the differences
sum_of_squares = sum(
[pow(prefs[item1][item] - prefs[item2][item], 2) for item in prefs[item1] if item in prefs[item2]])
return 1 / (1 + sqrt(sum_of_squares))
# Returns the Pearson correlation coefficient for p1 and p2
def sim_pearson(prefs, p1, p2):
# Get the list of mutually rated items
si = {}
for item in prefs[p1]:
if item in prefs[p2]: si[item] = 1
# if they are no ratings in common, return 0
if len(si) == 0: return 0
# Sum calculations
n = len(si)
# Sums of all the preferences
sum1 = float(sum([prefs[p1][it] for it in si]))
sum2 = float(sum([prefs[p2][it] for it in si]))
# Sums of the squares
sum1Sq = float(sum([pow(prefs[p1][it], 2) for it in si]))
sum2Sq = float(sum([pow(prefs[p2][it], 2) for it in si]))
# Sum of the products
pSum = float(sum([prefs[p1][it] * prefs[p2][it] for it in si]))
# Calculate r (Pearson score)
num = float(pSum - (sum1 * sum2 / n))
den = float(sqrt((sum1Sq - pow(sum1, 2) / n) * (sum2Sq - pow(sum2, 2) / n)))
if den == 0: return 0
r = float(num / den)
return round(r, 7)
def sim_pearson1(prefs, person1, person2):
#get the list of shared items
si = {}
for item in prefs[person1]:
if item in prefs[person2]:
si[item] = 1
#if they have no shared items, return 0
if len(si) == 0: return 0
#find the number of elements
n = len(si)
#add up all the prefs
sum1 = sum([prefs[person1][item] for item in si])
sum2 = sum([prefs[person2][item] for item in si])
#calculate the mean of the critics of p1 and p2
mean1 = sum1 / n;
mean2 = sum2 / n;
#calculate the covariance
covariance = sum([(prefs[person1][item] - mean1) * (prefs[person2][item] - mean2) for item in si]) / n
#calculate the standard_deviation
sd1 = sqrt(sum([pow(prefs[person1][item] - mean1, 2) for item in si]) / n)
sd2 = sqrt(sum([pow(prefs[person2][item] - mean2, 2) for item in si]) / n)
if sd1 * sd2 == 0: return 0
#calculate the pearson correlation improved
pearson = (covariance / (sd1 * sd2))
return pearson
def sim_pearson_improved(prefs, person1, person2):
#get the list of shared items
si = {}
for item in prefs[person1]:
if item in prefs[person2]:
si[item] = 1
#if they have no shared items, return 0
if len(si) == 0: return 0
#find the number of elements
n = len(si)
#get the count of items rated by person
count1 = 0
count2 = 0
for person in prefs[person1]:
count1 += 1
for item in prefs[person2]:
count2 += 1
totalCount = count1 + count2 - n
#add up all the prefs
sum1 = sum([prefs[person1][item] for item in si])
sum2 = sum([prefs[person2][item] for item in si])
#calculate the mean of the critics of p1 and p2
mean1 = sum1 / n;
mean2 = sum2 / n;
#calculate the covariance
covariance = sum([(prefs[person1][item] - mean1) * (prefs[person2][item] - mean2) for item in si]) / n
#calculate the standard_deviation
sd1 = sqrt(sum([pow(prefs[person1][item] - mean1, 2) for item in si]) / n)
sd2 = sqrt(sum([pow(prefs[person2][item] - mean2, 2) for item in si]) / n)
if sd1 * sd2 == 0: return 0
#calculate the pearson correlation improved
pearson = (covariance / (sd1 * sd2)) * (float(n) / float(totalCount))
#print n,count,float(n)/float(count),pearson
return pearson
def sim_cosine(prefs, item1, item2):
si = {}
for i in prefs[item1]:
if i in prefs[item2]:
si[i] = 1
#print si
if len(si) == 0: return 0
x = sqrt(sum([prefs[item1][it] ** 2 for it in si]))
y = sqrt(sum([prefs[item2][it] ** 2 for it in si]))
xy = sum([prefs[item1][it] * prefs[item2][it] for it in si])
cos = xy / (x * y)
return cos
def sim_cosine_improved(prefs, item1, item2):
si = {}
for i in prefs[item1]:
if i in prefs[item2]:
si[i] = 1
#print si
n = len(si)
if n == 0: return 0
count1 = 0
count2 = 0
for item in prefs[item1]:
count1 += 1
for item in prefs[item2]:
count2 += 1
totalCount = count1 + count2 - n
x = sqrt(sum([prefs[item1][it] ** 2 for it in si]))
y = sqrt(sum([prefs[item2][it] ** 2 for it in si]))
xy = sum([prefs[item1][it] * prefs[item2][it] for it in si])
cos = xy / (x * y)
return cos * (float(n) / float(totalCount))
def sim_Jaccard(s1, s2, length):
count = 0
for i in range(0, length):
if s1[i] == '1' and s2[i] == '1':
count += 1
if s1[i] == '1\n' and s2[i] == '1\n':
count += 1
return count / (length - count)
def sim_itemType(s1, s2, length):
count = 0
for i in range(0, length):
if s1[i] == '1' and s2[i] == '1':
count += 1
if s1[i] == '1\n' and s2[i] == '1\n':
count += 1
return count / 5
def sim_cosine_improved_tag(prefs, item1, item2, movieTags):
common = 0
for i in movieTags[item1]:
if i in movieTags[item2]:
common += 1
if common >= 5:
return 0.8
else:
si = {}
for i in prefs[item1]:
if i in prefs[item2]:
si[i] = 1
#print si
n = len(si)
if n == 0: return 0
count1 = 0
count2 = 0
for item in prefs[item1]:
count1 += 1
for item in prefs[item2]:
count2 += 1
totalCount = count1 + count2 - n
x = sqrt(sum([prefs[item1][it] ** 2 for it in si]))
y = sqrt(sum([prefs[item2][it] ** 2 for it in si]))
xy = sum([prefs[item1][it] * prefs[item2][it] for it in si])
cos = xy / (x * y)
return cos * (float(n) / float(totalCount))
#def sim_pearson_improved_typeAdded(prefs,item1,item2):
# pearson_improved=sim_pearson_improved(prefs,item1,item2)
# item_type=itemSimSet[item1][item2]
# return 0.9*(pearson_improved+1)/2.0+0.1*item_type