Item-Based Collaborative Filtering Recommendation

摘要：用户过去的偏好很可能展示或者反应未来的兴趣偏好。数据集我们选用，下载地址数据集算法理论算法框架如图，输入是的评分矩阵，该矩阵非常稀疏。所以预测分两步进行计算项目之间的相似性和根据相似性进行预测评分。

【参考文献】：Sarwar B M . Item-based collaborative filtering recommendation algorithms[C]// International Conference on World Wide Web. ACM, 2001.
背景：推荐领域必读文献之一，经典之作，本博客主要记录了该文章的主要思想和相关实现代码，欢迎观摩！

前提或假设

用户对项目的评分值，能够反应用户对项目某种程度上的偏好。

用户过去的偏好很可能展示或者反应未来的兴趣偏好。

数据集

我们选用MovieLens 100K Dataset，=> 100,000 ratings from 1000 users on 1700 movies.
下载地址：movielens数据集

算法理论
算法框架：如图，输入是user-item的评分矩阵，该矩阵非常稀疏。算法的任务是预测特定用户对特定项目的评分，填补矩阵中空白单元格，接着根据预测评分从高到低为特定用户进行top-N推荐

算法预测：算法认为某用户喜欢某项目，在很大程度上也会对和该项目较相似的项目产生兴趣。所以预测分两步进行：计算项目之间的相似性和根据相似性进行预测评分。
文章提供了三个相似性计算公式：
Cosine-based Similarity
$$ sim(i,j)= cos(vec{i},vec{j})= frac{vec{i}cdot vec{j}}{left | vec{i} ight |_{2}*left | vec{j} ight |_{2}} $$
Correlation-based Similarity
$$ sim(i,j)= frac{sum _{uin U}(R_{u,i}-ar{R}_{i})(R_{u,j}-ar{R}_{j})}{sqrt{sum _{uin U}(R_{u,i}-ar{R}_{i})^{2}}sqrt{sum _{uin U}(R_{u,j}-ar{R}_{j})^{2}}} $$
Adjusted Cosine Similarity
$$ sim(i,j)= frac{sum _{uin U}(R_{u,i}-ar{R}_{u})(R_{u,j}-ar{R}_{u})}{sqrt{sum _{uin U}(R_{u,i}-ar{R}_{u})^{2}}sqrt{sum _{uin U}(R_{u,j}-ar{R}_{u})^{2}}} $$
但是所有的相似性计算公式必须在共同评分项上进行，即同时评价过i和j的历史评分

算法选取和该项目最相似的前N个项目作为预测基础，预测公式如下：
$$ P_{u,i}=frac{sum _{all similar items,N}(S_{i,N}*R_{u,N})}{sum _{all similar items,N}(left | S_{i,N} ight |)} $$
算法最后一步，根据预测评分值从高到低进行推荐

实验度量
文章采用MAE进行误差度量，公式如下：
$$ MAE = frac{sum_{i=1}^{N}left | p_{i}-q_{i} ight |}{N} $$

Python 代码

# !usr/bin/python
# -*- coding=utf-8 -*-
import math
import operator
#加载数据
def loadData():
    # trainSet格式为： testSet格式一致
    # {
    #   userid:{
    #       itemid1: rating,
    #       itemid2: rating
    #   }
    # }
    # movieUser格式为：看过某一部电影的所有用户集合
    # {
    #   itemid: {
    #       userid1: rating,
    #       userid2: rating
    #   }
    # }
    # 
    # 
    # 
    trainSet = {}
    testSet = {}
    movieUser = {}

    TrainFile = "./dataset/u1.base"  # 指定训练集
    TestFile = "./dataset/u1.test"  # 指定测试集

    # 读取训练集
    f = open(TrainFile,"r")
    lines = f.readlines()
    for line in lines:
        arr = line.strip().split("	")
        userId = arr[0]
        itemId = arr[1]
        rating = arr[2]
        trainSet.setdefault(userId, {})
        trainSet[userId].setdefault(itemId, float(rating))
        movieUser.setdefault(itemId, {})
        movieUser[itemId].setdefault(userId, float(rating))

    # 读取测试集
    f1 = open(TestFile,"r")
    lines1 = f1.readlines()
    for line1 in lines1:
        arr1 = line1.strip().split("	")
        userId1 = arr1[0]
        itemId1 = arr1[1]
        rating1 = arr1[2]
        testSet.setdefault(userId1, {})
        testSet[userId1].setdefault(itemId1, float(rating1))

    arr = [trainSet,movieUser]
    return arr


# 生成电影电影共有用户矩阵
def i_j_users(i_id,j_id,movieUser):
    # ij_users格式为：
    # {
    #   (i_id,j_id):{userid1:None,userid2:None,....}
    # }
    if i_id in movieUser.keys():
        i_users = movieUser[i_id]
    else:
        i_users = {}
    if j_id in movieUser.keys():
        j_users = movieUser[j_id]
    else:
        j_users = {}
    
    inter = dict.fromkeys([x for x in i_users if x in j_users])
    i_j_users = {(i_id,j_id):inter}
    return i_j_users


#计算一个用户的平均分数
def getAverageRating(trainSet,userid):
    average = (sum(trainSet[userid].values()) * 1.0) / len(trainSet[userid].keys())
    return average

#计算项目相似度
def getItemSim(i_j_users,i_id,j_id,trainSet):
    # 分子 sumtop
    # 分母 sumbot1  sumbot2
    sumtop = 0
    sumbot1 = 0
    sumbot2 = 0
    ij_users = i_j_users[(i_id,j_id)]
    if not ij_users:
        ij_sim = -9999  # 疑问？ 为0 或者为None
    else:
        for user in ij_users.keys():
            avr_user = getAverageRating(trainSet,user)
            # 求分子
            left = trainSet[user][i_id] - avr_user
            right = trainSet[user][j_id] - avr_user
            sumtop += left*right
            # 求分母
            sumbot1 += left*left
            sumbot2 += right*right      
    if sumbot1 == 0 or sumbot2 == 0:
        ij_sim = 1
    else:
        ij_sim = sumtop*1.0 / (math.sqrt(sumbot1)*math.sqrt(sumbot2))
    
    return ij_sim

# 计算项目i和其她所有项目的相似度并排序
# i_allitem_sim格式为：
# {
#     j_id1:s1,
#     j_id2:s2
# }
def i_allitem_sort(i_id,movieUser,trainSet,N):
    i_allitem = {}
    for j in movieUser.keys():
        if j != i_id:
            i_j_user = i_j_users(i_id,j,movieUser)
            s = getItemSim(i_j_user,i_id,j,trainSet)
            i_allitem.setdefault(j, s)

    i_allitem_sort1 = sorted(i_allitem.items(), key = operator.itemgetter(1), reverse = True)[0:N]
    i_allitem_sort_dict = {}
    for n in range(len(i_allitem_sort1)):
        j1 = i_allitem_sort1[n][0]
        s = i_allitem_sort1[n][1]
        i_allitem_sort_dict.setdefault(j1, s)
    return i_allitem_sort_dict

# 预测评分
def prediction(userid,itemid,moviUser,trainSet,N):
    # predict 格式为：
    # {
    #   (userid,itemid): pui
    # }
    predict = 0
    sumtop = 0
    sumbot = 0
    nsets = i_allitem_sort(itemid,movieUser,trainSet,N)
    for j in nsets.keys():
        # 防止用户对i的领域集合内的j没评分
        if j not in trainSet[userid].keys():
            ruj = 0
            mid = 0
        else:
            ruj = trainSet[userid][j]
            mid = abs(nsets[j])
        sumtop += nsets[j]*ruj
        sumbot += mid
    # 防止分母为0 
    if sumbot == 0:
        predict = 0
    else:
        predict = sumtop * 1.0 / sumbot
    return predict

def saveFile(moviUser,trainSet,N):
    # 读取用户
    string = ""
    # 正在读取
    f = open("../Collaborative Filtering/dataset/u1.test")
    fw = open("../Collaborative Filtering/predict","w")
    fl = f.readlines()
    for i in fl:
        arr = i.split("	")
        uid = str(arr[0].strip())
        item = str(arr[1].strip())
        rating = float(arr[2].strip())
        predictScore = prediction(str(uid),str(item),moviUser,trainSet,N)
        string = string + str(uid) + "	" + str(item) + "	" + str(rating) + "	" + str(predictScore) + "
"
    fw.write(string)
    f.close()
    fw.close()
    
# 计算预测分析准确度
def getMAE():
    f = open("../Collaborative Filtering/predict")
    fl = f.readlines()
    mae = 0.0
    s = 0
    counttest = 0# 测试集的个数
    for i in fl:
        arr = i.split("	")
        uid = str(arr[0].strip())
        item = str(arr[1].strip())
        rating = float(arr[2].strip())
        predictScore = float(arr[3].strip())
        if predictScore == 0:
            mid = 0
        else:
            mid = abs((predictScore-rating))
            counttest = counttest + 1
        s = s + mid 
    mae = s/counttest
    print(mae)        


if __name__ == "__main__":

    N = 30
    arr = loadData()
    trainSet = arr[0]
    movieUser = arr[1]
    saveFile(movieUser,trainSet,N)
    # getMAE()