在现实情况下，用户的显式反馈严重不足，但一般拥有大量隐式反馈信息。所以在偏置svd基础上增加了用户的隐式反馈信息，该方法融合了用户的显式和隐式信息。
1.预测评分公式为
其中，有全局平均分，user的偏置信息，item的偏置信息，Ni为该用户评价过的所有item集合，
从隐式反馈出发，作为用户偏好的补充，ys为隐式偏好。
2.损失函数为平方误差+L2正则项，其中
是真实评分。
3.利用SGD训练更新，其中
。
4.程序，(数据movielens 100k，https://github.com/jiangnanboy/recommendation_methods/blob/master/com/sy/reco/recommendation/matrix_factorization/svdpp.py)
import numpy as np
import math
‘‘‘
融合了BiasLFM以及用户的隐式行为
‘‘‘
class SVDPP():
‘‘‘
初始化ratingMatrix,F, alpha, λ
ratingMatrix:评分矩阵
F:隐因子数目
alpha:学习速率
λ:正则化参数，以防过拟合
‘‘‘
def __init__(self, ratingMatrix, F, alpha, λ):
self.ratingMatrix = ratingMatrix
self.F = F
self.alpha = alpha
self.λ = λ
# 对U,I,Y矩阵初始化，随机填充，根据经验随机数与1/sqrt(F)成正比,bu向量与bi向量初始化为全0,u是所有有评分的全局平均
def __initPQ(self, userSum, itemSum):
self.U = np.zeros((userSum, self.F))
self.I = np.zeros((itemSum, self.F))
self.Y=np.zeros((itemSum,self.F))
self.bu = np.zeros(userSum)
self.bi = np.zeros(itemSum)
self.meanV = np.mean(self.ratingMatrix[self.ratingMatrix > 0]) # 全局均值
for i in range(userSum):
self.U[i] = [np.random.random() / math.sqrt(self.F) for x in range(self.F)]
for i in range(itemSum):
self.I[i] = [np.random.random() / math.sqrt(self.F) for x in range(self.F)]
self.Y[i]=[np.random.random()/math.sqrt(self.F) for x in range(self.F)]
# 迭代训练分解，max_iter:迭代次数
def iteration_train(self, max_iter):
userSum = len(self.ratingMatrix) # 用户个数
itemSum = len(self.ratingMatrix[0]) # 项目个数
self.__initPQ(userSum, itemSum) # 初始化U,I,Y,bu,bi
Z=np.zeros((userSum,self.F))
for step in range(max_iter):
for user in range(userSum):
Z[user]=self.U[user]
ru=1/math.sqrt(len(self.U[user][self.U[user,:]>0]))#1/sqrt(Usum>0)用户评过分的项目个数
for item in range(itemSum):
if self.ratingMatrix[user, item] > 0: # 未评分的项目不参与计算
for f in range(self.F):
Z[user,f]+=self.Y[item,f]*ru #I更新中的部分(1/sqrt(Usum))*self.Y
sum=np.zeros(self.F)
for item in range(itemSum):
if self.ratingMatrix[user,item]>0:# 未评分的项目不参与计算
eui = self.ratingMatrix[user, item] - self.predict(user, item,ru) # 真实值减去预测的值
self.bu[user] += self.alpha * (eui - self.λ * self.bu[user]) # 更新bu
self.bi[item] += self.alpha * (eui - self.λ * self.bi[item]) # 更新bi
for f in range(self.F):
sum[f]+=self.I[item,f]*eui*ru #Y更新中的部分eui*ru*I
self.U[user, f] += self.alpha * (self.I[item, f] * eui - self.λ * self.U[user, f]) # 更新U
self.I[item,f]+=self.alpha*(eui*(self.U[user,f]+Z[user,f])-self.λ*self.I[item,f])#更新I
#更新Y
for item in range(itemSum):
for f in range(self.F):
self.Y[item,f]+=self.alpha*(sum[f]-self.λ*self.Y[item,f])
#self.alpha*=0.9
predictRating = []#存放全部预测数据
for user in range(userSum):
userItemRating = []
ru = 1 / math.sqrt(len(self.U[user][self.U[user, :] > 0])) # 1/sqrt(Usum>0)用户评过分的项目个数
for item in range(itemSum):
pui = self.predict(user, item,ru)
userItemRating.append(pui)
predictRating.append(userItemRating)
return np.round(np.array(predictRating), 0)
#预测打分，用户的行与项目的列
def predict(self,user,item,ru):
z=np.zeros(self.F)
for i in range(len(self.ratingMatrix[user])):
if self.ratingMatrix[user,i]>0:
for f in range(self.F):
z[f]+=self.Y[i,f]
pui =0.
for f in range(self.F):
pui+=(self.U[user,f]+z[f]/ru)*self.I[item,f]
pui+=self.meanV+self.bu[user]+self.bi[item]
return pui
# 预测误差训练，convergence:误差收敛，小于这个误差,则终止训练
def convergence_train(self, convergence):
userSum = len(self.ratingMatrix) # 用户个数
itemSum = len(self.ratingMatrix[0]) # 项目个数
self.__initPQ(userSum, itemSum) # 初始化U,I,Y,bu,bi
Z = np.zeros((userSum, self.F))
flag=True
while flag:
for user in range(userSum):
Z[user] = self.U[user]
ru = 1 / math.sqrt(len(self.U[user][self.U[user, :] > 0])) # 1/sqrt(Usum>0)用户评过分的项目个数
for item in range(itemSum):
if self.ratingMatrix[user, item] > 0: # 未评分的项目不参与计算
for f in range(self.F):
Z[user, f] += self.Y[item, f] * ru # I更新中的部分(1/sqrt(Usum))*self.Y
sum = np.zeros(self.F)
for item in range(itemSum):
if self.ratingMatrix[user, item] > 0: # 未评分的项目不参与计算
eui = self.ratingMatrix[user, item] - self.predict(user, item, ru) # 真实值减去预测的值
self.bu[user] += self.alpha * (eui - self.λ * self.bu[user]) # 更新bu
self.bi[item] += self.alpha * (eui - self.λ * self.bi[item]) # 更新bi
for f in range(self.F):
sum[f] += self.I[item, f] * eui * ru # Y更新中的部分eui*ru*I
self.U[user, f] += self.alpha * (self.I[item, f] * eui - self.λ * self.U[user, f]) # 更新U
self.I[item, f] += self.alpha * (
eui * (self.U[user, f] + Z[user, f]) - self.λ * self.I[item, f]) # 更新I
# 更新Y
for item in range(itemSum):
for f in range(self.F):
self.Y[item, f] += self.alpha * (sum[f] - self.λ * self.Y[item, f])
cost = 0 # 误差
for user in range(userSum):
ru = 1 / math.sqrt(len(self.U[user][self.U[user, :] > 0])) # 1/sqrt(Usum>0)用户评过分的项目个数
for item in range(itemSum):
if self.ratingMatrix[user, item] > 0:
cost += (1 / 2) * math.pow(self.ratingMatrix[user, item] - self.predict(user, item,ru), 2)
cost += (1 / 2) * self.λ * (math.pow(self.bu[user], 2) + math.pow(self.bi[item], 2))
for f in range(self.F):
cost += (1 / 2) * self.λ * (math.pow(self.U[user, f], 2) + math.pow(self.I[item, f], 2)+math.pow(self.Y[item,f],2))
if cost < convergence:
flag = False
predictRating = [] # 存放全部预测数据
for user in range(userSum):
userItemRating = []
ru = 1 / math.sqrt(len(self.U[user][self.U[user, :] > 0])) # 1/sqrt(Usum>0)用户评过分的项目个数
for item in range(itemSum):
pui = self.predict(user, item, ru)
userItemRating.append(pui)
predictRating.append(userItemRating)
return np.round(np.array(predictRating), 0)
原文地址：https://www.cnblogs.com/little-horse/p/12499671.html
时间： 2024-10-11 15:57:21