基于邻域的推荐算法

本文主要是介绍基于邻域的推荐算法，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

User-Based

1. 用户相似度：
   $$w_{uv}=\frac{|N(u)\cap N(v)|}{|N(u)\cup N(v)|}$$
   $$w_{uv}=\frac{|N(u)\cap N(v)|}{\sqrt{|N(u)||N(v)|}}$$
2. 建立物品-用户倒排表，转化为用户相似度矩阵：

def UserSimilarity(train):# build inverse table for item_usersitem_users = dict()for u, items in train.items():for i in items.keys():if i not in item_users:item_users[i] = set()item_users[i].add(u)#calculate co-rated items between usersC = dict()N = dict()for i, users in item_users.items():for u in users:N[u] += 1for v in users:if u == v:continueC[u][v] += 1#calculate finial similarity matrix WW = 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

3. UserCF下用户$u$对物品$i$的感兴趣程度，$S(u,k)$是和用户$u$相似度最接近的$K$个用户，$N(i)$是对物品$i$有过行为的用户集合：
   $$p(u,i)=\sum _{v\in S(u,K)\cap N(i)}{w}_{uv}{r}_{vi}$$
4. 代码实现：

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 beforecontinuerank[i] += wuv * rvireturn rank

5. 改进用户相似度计算公式：
   $$w_{uv}=\frac{|N(u)\cap N(v)|}{\sqrt{|N(u)||N(v)|}}$$

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