基於使用者的協同過濾演算法
阿新 • • 發佈：2018-12-17
基本思想
俗話說“物以類聚、人以群分”，拿看電影這個例子來說，如果你喜歡《蝙蝠俠》、《碟中諜》、《星際穿越》、《原始碼》等電影，另外有個人也都喜歡這些電影，而且他還喜歡《鋼鐵俠》，則很有可能你也喜歡《鋼鐵俠》這部電影。
所以說，當一個使用者 A 需要個性化推薦時，可以先找到和他興趣相似的使用者群體 G，然後把 G 喜歡的、並且 A 沒有聽說過的物品推薦給 A，這就是基於使用者的系統過濾演算法。
原理
根據上述基本原理，我們可以將基於使用者的協同過濾推薦演算法拆分為兩個步驟：
- 找到與目標使用者興趣相似的使用者集合
- 找到這個集合中使用者喜歡的、並且目標使用者沒有聽說過的物品推薦給目標使用者
1、發現興趣相似的使用者
通常用 Jaccard 公式或者餘弦相似度計算兩個使用者之間的相似度。設 N(u) 為使用者 u 喜歡的物品集合，N(v) 為使用者 v 喜歡的物品集合，那麼 u 和 v 的相似度是多少呢：
Jaccard 公式：
餘弦相似度：
假設目前共有4個使用者： A、B、C、D；共有5個物品：a、b、c、d、e。使用者與物品的關係（使用者喜歡物品）如下圖所示：
如何一下子計算所有使用者之間的相似度呢？為計算方便，通常首先需要建立“物品—使用者”的倒排表，如下圖所示：
到此，計算使用者相似度就大功告成，可以很直觀的找到與目標使用者興趣較相似的使用者。
2、推薦物品
首先需要從矩陣中找出與目標使用者 u 最相似的 K 個使用者，用集合 S(u, K) 表示，將 S 中使用者喜歡的物品全部提取出來，並去除 u 已經喜歡的物品。對於每個候選物品 i ，使用者 u 對它感興趣的程度用如下公式計算：
舉個例子，假設我們要給 A 推薦物品，選取 K = 3 個相似使用者，相似使用者則是：B、C、D，那麼他們喜歡過並且 A 沒有喜歡過的物品有：c、e，那麼分別計算 p(A, c) 和 p(A, e)：
python程式碼
# -*- coding: utf-8 -*-
"""
Created on Wed Oct 24 17:07:29 2018
@author: Administrator
"""
import random
import math
class UserBasedCF:
def __init__(self,datafile = None):
self.datafile = datafile
self.readData()
self.splitData(3,47)
def readData(self,datafile = None):
"""
read the data from the data file which is a data set
"""
self.datafile = datafile or self.datafile
self.data = []
for line in open(self.datafile):
userid,itemid,record,_ = line.split()
self.data.append((userid,itemid,int(record)))
def splitData(self,k,seed,data=None,M = 8):
"""
split the data set
testdata is a test data set
traindata is a train set
test data set ： train data set ＝ 1:M-1
"""
self.testdata = {}
self.traindata = {}
data = data or self.data
random.seed(seed)
for user,item, record in self.data:
if random.randint(0,M) == k:
self.testdata.setdefault(user,{})
self.testdata[user][item] = record
else:
self.traindata.setdefault(user,{})
self.traindata[user][item] = record
def userSimilarity(self,train = None):
"""
One method of getting user similarity matrix
"""
train = train or self.traindata
self.userSim = dict()
for u in train.keys():
for v in train.keys():
if u == v:
continue
self.userSim.setdefault(u,{})
self.userSim[u][v] = len(set(train[u].keys()) & set(train[v].keys()))
self.userSim[u][v] /=math.sqrt(len(train[u]) * len(train[v]) *1.0)
def userSimilarityBest(self,train = None):
"""
the other method of getting user similarity which is better than above
you can get the method on page 46
In this experiment，we use this method
"""
train = train or self.traindata
self.userSimBest = dict()
item_users = dict()
for u,item in train.items():
for i in item.keys():
item_users.setdefault(i,set())
item_users[i].add(u)
user_item_count = dict()
count = dict()
for item,users in item_users.items():
for u in users:
user_item_count.setdefault(u,0)
user_item_count[u] += 1
for v in users:
if u == v:continue
count.setdefault(u,{})
count[u].setdefault(v,0)
count[u][v] += 1
for u ,related_users in count.items():
self.userSimBest.setdefault(u,dict())
for v, cuv in related_users.items():
self.userSimBest[u][v] = cuv / math.sqrt(user_item_count[u] * user_item_count[v] * 1.0)
def recommend(self,user,train = None,k = 8,nitem = 40):
train = train or self.traindata
rank = dict()
interacted_items = train.get(user,{})
for v ,wuv in sorted(self.userSimBest[user].items(),key = lambda x : x[1],reverse = True)[0:k]:
for i , rvi in train[v].items():
if i in interacted_items:
continue
rank.setdefault(i,0)
rank[i] += wuv * rvi
return dict(sorted(rank.items(),key = lambda x :x[1],reverse = True)[0:nitem])
def recallAndPrecision(self,train = None,test = None,k = 8,nitem = 10):
"""
Get the recall and precision, the method you want to know is listed
in the page 43
"""
train = train or self.traindata
test = test or self.testdata
hit = 0
recall = 0
precision = 0
for user in train.keys():
tu = test.get(user,{})
rank = self.recommend(user, train = train,k = k,nitem = nitem)
for item,_ in rank.items():
if item in tu:
hit += 1
recall += len(tu)
precision += nitem
return (hit / (recall * 1.0),hit / (precision * 1.0))
def coverage(self,train = None,test = None,k = 8,nitem = 10):
train = train or self.traindata
test = test or self.testdata
recommend_items = set()
all_items = set()
for user in train.keys():
for item in train[user].keys():
all_items.add(item)
rank = self.recommend(user, train, k = k, nitem = nitem)
for item,_ in rank.items():
recommend_items.add(item)
return len(recommend_items) / (len(all_items) * 1.0)
def popularity(self,train = None,test = None,k = 8,nitem = 10):
"""
Get the popularity
the algorithm on page 44
"""
train = train or self.traindata
test = test or self.testdata
item_popularity = dict()
for user ,items in train.items():
for item in items.keys():
item_popularity.setdefault(item,0)
item_popularity[item] += 1
ret = 0
n = 0
for user in train.keys():
rank = self.recommend(user, train, k = k, nitem = nitem)
for item ,_ in rank.items():
ret += math.log(1+item_popularity[item])
n += 1
return ret / (n * 1.0)
def testRecommend():
ubcf = UserBasedCF('data.txt')
ubcf.readData()
ubcf.splitData(4,100)
ubcf.userSimilarity()
user = "345"
rank = ubcf.recommend(user,k = 3)
for i,rvi in rank.items():
items = ubcf.testdata.get(user,{})
record = items.get(i,0)
print ("%5s: %.4f--%.4f" %(i,rvi,record))
def testUserBasedCF():
cf = UserBasedCF('data.txt')
cf.userSimilarityBest()
print ("%3s%20s%20s%20s%20s" % ('K',"recall",'precision','coverage','popularity'))
for k in [5,10,20,40,80,160]:
recall,precision = cf.recallAndPrecision( k = k)
coverage = cf.coverage(k = k)
popularity = cf.popularity(k = k)
print ("%3d%19.3f%%%19.3f%%%19.3f%%%20.3f" % (k,recall * 100,precision * 100,coverage * 100,popularity))
if __name__ == "__main__":
testUserBasedCF()