# 推荐系统实践--基于用户的协同过滤算法

## 基于用户的协同过滤算法

(1) 找到和目标用户兴趣相似的用户集合。

(2) 找到这个集合中的用户喜欢的，且目标用户没有听说过的物品推荐给目标用户。

jaccard                                                                             余项公式：

```def UserSimilarity(train):
W = dict()
for u in train.keys():
for v in train.keys():
if u == v:
continue
W[u][v] = len(train[u] & train[v])
W[u][v] = /= math.sqrt(len(train[u]) * len(train[v]) * 1.0)
return W```

```def UserSimilarity(train):
# build inverse table for item_users
item_users = dict()
for u, items in train.items():
for i in items.keys():
if i not in item_users:
item_users[i] = set()
#calculate co-rated items between users
C = dict()
N = dict()
for i, users in item_users.items():
for u in users:
N[u] += 1
for v in users:
if u == v:
continue
C[u][v] += 1
#calculate finial similarity matrix W
W = dict()
for u, related_users in C.items():
for v, cuv in related_users.items():
W[u][v] = cuv / math.sqrt(N[u] * N[v])
return W
```

```def Recommend(user, train, W):
rank = dict()
interacted_items = train[user]
for v, wuv in sorted(W[u].items, key=itemgetter(1), reverse=True)[0:K]:
for i, rvi in train[v].items:
if i in interacted_items:
#we should filter items user interacted before
continue
rank[i] += wuv * rvi
return rank```

## 用户相似度计算的改进

```def UserSimilarity(train):
# build inverse table for item_users
item_users = dict()
for u, items in train.items():
for i in items.keys():
if i not in item_users:
item_users[i] = set()
#calculate co-rated items between users
C = dict()
N = dict()
for i, users in item_users.items():
for u in users:
N[u] += 1
for v in users:
if u == v:
continue
C[u][v] += 1 / math.log(1 + len(users))
#calculate finial similarity matrix W
W = dict()
for u, related_users in C.items():
for v, cuv in related_users.items():
W[u][v] = cuv / math.sqrt(N[u] * N[v])
return W
```