import math
def UserSimilarity(train):
item_users = dict()
for u,items in train.items():
for i in items:
if i not in item_users:
item_users[i]=set()
item_users[i].add(u)
print item_users
#{'a': set(['A', 'B']), 'c': set(['B', 'D']), 'b': set(['A', 'C']), 'e': set(['C', 'D']), 'd': set(['A', 'D'])}
C = dict()
N = dict()
for i , users in item_users.items():
for u in users:
N.setdefault(u,0)
N[u] += 1
for v in users:
if u == v:
continue
C.setdefault(u,{})
C[u].setdefault(v,0)
C[u][v] += 1
print C
print N
#{'A': {'C': 1, 'B': 1, 'D': 1}, 'C': {'A': 1, 'D': 1}, 'B': {'A': 1, 'D': 1}, 'D': {'A': 1, 'C': 1, 'B': 1}}
#{'A': 3, 'C': 2, 'B': 2, 'D': 3}
W = dict()
for u , related_users in C.items():
for v , cuv in related_users.items():
W.setdefault(u,{})
W[u].setdefault(v,0)
W[u][v] = cuv / math.sqrt(N[u] * N[v])
return W
train={'A':['a','b','d'],'B':['a','c'],'C':['b','e'],'D':['c','d','e']}
F = UserSimilarity(train)
print F
#{'A': {'C': 0.4082482904638631, 'B': 0.4082482904638631, 'D': 0.3333333333333333}, 'C': {'A': 0.4082482904638631, 'D': 0.4082482904638631}, 'B': {'A': 0.4082482904638631, 'D': 0.4082482904638631}, 'D': {'A': 0.3333333333333333, 'C': 0.4082482904638631, 'B': 0.4082482904638631}}
