摘要：用戶過去的偏好很可能展示或者反應未來的興趣偏好。數據集我們選用，下載地址數據集算法理論算法框架如圖，輸入是的評分矩陣，該矩陣非常稀疏。所以預測分兩步進行計算項目之間的相似性和根據相似性進行預測評分。

【參考文獻】：Sarwar B M . Item-based collaborative filtering recommendation algorithms[C]// International Conference on World Wide Web. ACM, 2001.
背景：推薦領域必讀文獻之一，經典之作，本博客主要記錄了該文章的主要思想和相關實現代碼，歡迎觀摩！

前提或假設

用戶對項目的評分值，能夠反應用戶對項目某種程度上的偏好。

用戶過去的偏好很可能展示或者反應未來的興趣偏好。

數據集

我們選用MovieLens 100K Dataset，=> 100,000 ratings from 1000 users on 1700 movies.
下載地址：movielens數據集

算法理論
算法框架：如圖，輸入是user-item的評分矩陣，該矩陣非常稀疏。算法的任務是預測特定用戶對特定項目的評分，填補矩陣中空白單元格，接著根據預測評分從高到低為特定用戶進行top-N推薦

算法預測：算法認為某用戶喜歡某項目，在很大程度上也會對和該項目較相似的項目產生興趣。所以預測分兩步進行：計算項目之間的相似性和根據相似性進行預測評分。
文章提供了三個相似性計算公式：
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
$$ sim(i,j)= frac{sum _{uin U}(R_{u,i}-ar{R}_{u})(R_{u,j}-ar{R}_{u})}{sqrt{sum _{uin U}(R_{u,i}-ar{R}_{u})^{2}}sqrt{sum _{uin U}(R_{u,j}-ar{R}_{u})^{2}}} $$
但是所有的相似性計算公式必須在共同評分項上進行，即同時評價過i和j的歷史評分

算法選取和該項目最相似的前N個項目作為預測基礎，預測公式如下：
$$ P_{u,i}=frac{sum _{all similar items,N}(S_{i,N}*R_{u,N})}{sum _{all similar items,N}(left | S_{i,N} ight |)} $$
算法最后一步，根據預測評分值從高到低進行推薦

實驗度量
文章采用MAE進行誤差度量，公式如下：
$$ MAE = frac{sum_{i=1}^{N}left | p_{i}-q_{i} ight |}{N} $$

Python 代碼

# !usr/bin/python
# -*- coding=utf-8 -*-
import math
import operator
#加載數據
def loadData():
    # trainSet格式為： testSet格式一致
    # {
    #   userid:{
    #       itemid1: rating,
    #       itemid2: rating
    #   }
    # }
    # movieUser格式為：看過某一部電影的所有用戶集合
    # {
    #   itemid: {
    #       userid1: rating,
    #       userid2: rating
    #   }
    # }
    # 
    # 
    # 
    trainSet = {}
    testSet = {}
    movieUser = {}

    TrainFile = "./dataset/u1.base"  # 指定訓練集
    TestFile = "./dataset/u1.test"  # 指定測試集

    # 讀取訓練集
    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))

    # 讀取測試集
    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


# 生成電影電影共有用戶矩陣
def i_j_users(i_id,j_id,movieUser):
    # ij_users格式為：
    # {
    #   (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


#計算一個用戶的平均分數
def getAverageRating(trainSet,userid):
    average = (sum(trainSet[userid].values()) * 1.0) / len(trainSet[userid].keys())
    return average

#計算項目相似度
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  # 疑問？ 為0 或者為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

# 計算項目i和其她所有項目的相似度并排序
# i_allitem_sim格式為：
# {
#     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

# 預測評分
def prediction(userid,itemid,moviUser,trainSet,N):
    # predict 格式為：
    # {
    #   (userid,itemid): pui
    # }
    predict = 0
    sumtop = 0
    sumbot = 0
    nsets = i_allitem_sort(itemid,movieUser,trainSet,N)
    for j in nsets.keys():
        # 防止用戶對i的領域集合內的j沒評分
        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
    # 防止分母為0 
    if sumbot == 0:
        predict = 0
    else:
        predict = sumtop * 1.0 / sumbot
    return predict

def saveFile(moviUser,trainSet,N):
    # 讀取用戶
    string = ""
    # 正在讀取
    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()
    
# 計算預測分析準確度
def getMAE():
    f = open("../Collaborative Filtering/predict")
    fl = f.readlines()
    mae = 0.0
    s = 0
    counttest = 0# 測試集的個數
    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()