相似性度量方法

欧几里得相似度

# Returns a distance-based similarity score for person1 and person2
def sim_distance(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 ratings in common, return 0
if len(si)==0: return 0

# Add up the squares of all the differences
sum_of_squares=sum([pow(prefs[person1][item]-prefs[person2][item],2)
for item in prefs[person1] if item in prefs[person2]])

return 1/(1+sum_of_squares)

皮尔逊相似度

# 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=sum([prefs[p1][it] for it in si])
sum2=sum([prefs[p2][it] for it in si])

# Sums of the squares
sum1Sq=sum([pow(prefs[p1][it],2) for it in si])
sum2Sq=sum([pow(prefs[p2][it],2) for it in si])

# Sum of the products
pSum=sum([prefs[p1][it]*prefs[p2][it] for it in si])

# Calculate r (Pearson score)
num=pSum-(sum1*sum2/n)
den=sqrt((sum1Sq-pow(sum1,2)/n)*(sum2Sq-pow(sum2,2)/n))
if den==0: return 0

r=num/den

return r

Tanimoto系数

#代表交集与并集的比率
def tanamoto(v1,v2):
c1,c2,shr=0,0,0

for i in range(len(v1)):
if v1[i]!=0: c1+=1 # in v1
if v2[i]!=0: c2+=1 # in v2
if v1[i]!=0 and v2[i]!=0: shr+=1 # in both

return 1.0-(float(shr)/(c1+c2-shr))