【推荐系统】SVD++
用户对物品的评分等操作实际上很少，但是用户的点击，关注，收藏，浏览时长等隐性行为却很多，能否将这些考虑进来作为我们的预测准则之一呢？
SVD++在RSVD的基础上，考虑了用户对物品的隐式行为。因为有时候一个用户的点击，收藏，浏览时长等隐式行为，我们是可以将其考虑进来的，它作为一种交互，也反应了用户的一种隐式意愿。为了将隐式兴趣加入到模型中，在预测规则中加入
r ^ u i = U u . V i . T + U ˉ u . V i . T + b u + b i + μ \hat r_{ui}=U_{u.}V_{i.}^T+\bar U_{u.}V^T_{i.}+b_u+b_i+\mu r^ui=Uu.Vi.T+Uˉu.Vi.T+bu+bi+μ
其中
U ˉ u . = 1 ∣ I ~ u ∣ ∑ i ′ ∈ I ~ u W i ′ . \bar U_{u.}=\frac{1}{\sqrt{|\widetilde I_u|}}\sum\limits_{i' \in \widetilde I_u}W_{i'.} Uˉu.=∣I u∣1i′∈I u∑Wi′.
\widetilde I_u其中 I ~ u \widetilde I_u I u表示用户u有交互过的商品， W i . W_{i.} Wi.是跟 U i . U_{i.} Ui.和 V i . V_{i.} Vi.相同维度的向量。同时，为了训练隐式意愿的权重W，避免过拟合，加入对应变量的正则项，目标函数变为
min θ ∑ u = 1 n ∑ i = 1 m y u i [ 1 2 ( r u i − r ^ u i ) 2 + α u 2 ∣ ∣ U u . ∣ ∣ 2 + α v 2 ∣ ∣ v i . ∣ ∣ 2 + β u 2 ∣ ∣ b u ∣ ∣ 2 + β v 2 ∣ ∣ b i ∣ ∣ 2 + β w 2 ∣ ∣ W i . ∣ ∣ 2 ] \min_\theta \sum_{u=1}^n\sum_{i=1}^my_{ui}\left[\frac{1}{2}(r_{ui}-\hat r_{ui})^2+\frac{\alpha_u}{2}||U_{u.}||^2+\frac{\alpha_v}{2}||v_{i.}||^2+\frac{\beta_u}{2}||b_u||^2+\frac{\beta_v}{2}||b_i||^2+\frac{\beta_w}{2}||W_{i.}||^2\right] θminu=1∑ni=1∑myui[21(rui−r^ui)2+2αu∣∣Uu.∣∣2+2αv∣∣vi.∣∣2+2βu∣∣bu∣∣2+2βv∣∣bi∣∣2+2βw∣∣Wi.∣∣2]
令 e u i = r u i − r ^ u i e_{ui}=r_{ui}-\hat r_{ui} eui=rui−r^ui，对变量 θ = ( U u . , V i . , b u , b i , W i ′ . ) \theta=(U_{u.},V_{i.},b_u,b_i,W_{i'.}) θ=(Uu.,Vi.,bu,bi,Wi′.)求偏导，有
∇ μ = − e u i ∇ b u = − e u i + β u b u ∇ b i = − e u i + β v b i ∇ U u . = − e u i V i . + α u U u . ∇ V i . = − e u i ( U u . + ( 1 ∣ I ~ u ∣ ∑ i ′ ∈ I ~ u W i ′ . ) ) + α v V i . ∇ W i ′ . = − e u i 1 ∣ I ~ u ∣ V i . + α w W i ′ . , i ∈ I ~ u \begin{aligned} &\nabla_\mu=-e_{ui}\\ &\nabla b_u=-e_{ui}+\beta_ub_u \\ &\nabla b_i= -e_{ui}+\beta_vb_i \\ &\nabla U_{u.}=-e_{ui}V_{i.}+\alpha_uU_{u.} \\ &\nabla V_{i.}=-e_{ui}(U_{u.}+(\frac{1}{\sqrt{|\widetilde I_u|}}\sum\limits_{i' \in \widetilde I_u}W_{i'.}))+\alpha_vV_{i.}\\ &\nabla W_{i'.}=-e_{ui}\frac{1}{\sqrt{|\widetilde I_u|}}V_{i.}+\alpha_wW_{i'.},i \in \widetilde I_u \end{aligned} ∇μ=−eui∇bu=−eui+βubu∇bi=−eui+βvbi∇Uu.=−euiVi.+αuUu.∇Vi.=−eui(Uu.+(∣I u∣1i′∈I u∑Wi′.))+αvVi.∇Wi′.=−eui∣I u∣1Vi.+αwWi′.,i∈I u
使用SGD算法，求解上面的参数直至收敛即可。SVD++算法在小数据集上表现和RSVD差不多，但是在大数据集上的表现要由于RSVD。
附实现代码：
import random
import math
import pandas as pd
import numpy as np
import math
class SVDplusplus():
def __init__(self, allfile, trainfile, testfile, latentFactorNum=20,alpha_u=0.01,alpha_v=0.01,alpha_w=0.01,beta_u=0.01,beta_v=0.01,learning_rate=0.01):
data_fields = ['user_id', 'item_id', 'rating', 'timestamp']
# all data file
allData = pd.read_table(allfile, names=data_fields)
user_list=sorted(set(allData['user_id'].values))
item_list=sorted(set(allData['item_id'].values))
ua_base=allData.sample(n=90570,replace=False)
self.test_df=allData.drop(ua_base.index,axis=0)
#ua_base_implict only have (user_id,item_id)
self.ua_base_implcit=ua_base.sample(frac=0.5,replace=False)
self.ua_base_explict=ua_base.drop(self.ua_base_implcit.index,axis=0)
self.implict=self.ua_base_implcit.pivot(index='user_id', columns='item_id', values='rating')
print(self.test_df.shape)
print(self.ua_base_explict.shape)
print(self.ua_base_implcit.shape)
data_df = pd.DataFrame(index=user_list, columns=item_list)
rating_matrix=self.ua_base_explict.pivot(index='user_id', columns='item_id', values='rating')
data_df.update(rating_matrix)
self.rating_matrix=data_df
# training set file
#self.train_df = pd.read_table(trainfile, names=data_fields)
# testing set file
#self.test_df=pd.read_table(testfile, names=data_fields)
# get factor number
self.latentFactorNum = latentFactorNum
# get user number
self.userNum = len(set(allData['user_id'].values))
# get item number
self.itemNum = len(set(allData['item_id'].values))
# learning rate
self.learningRate = learning_rate
# the regularization lambda
self.alpha_u=alpha_u
self.alpha_v=alpha_v
self.alpha_w=alpha_w
self.beta_u=beta_u
self.beta_v=beta_v
# initialize the model and parameters
self.initModel()
# initialize all parameters
def initModel(self):
self.mu = self.ua_base_explict['rating'].mean()
self.bu=(self.rating_matrix-self.mu).sum(axis=1)/self.rating_matrix.count(axis=1)
self.bu=self.bu.values#dataFrame转numpy
print(self.bu.shape)
self.bi = (self.rating_matrix - self.mu).sum() / self.rating_matrix.count()
self.bi = self.bi.values # dataFrame转numpy
self.bi[np.isnan(self.bi)]=0 #填充缺失值
# r = (np.random.random(1)[0]-0.05)*0.01
# np.mat((np.random.rand(self.userNum, self.latentFactorNum)-0.05)*0.01)
self.U = np.mat((np.random.rand(self.userNum, self.latentFactorNum)-0.05)*0.01)
self.V = np.mat((np.random.rand(self.itemNum, self.latentFactorNum)-0.05)*0.01)
self.W = np.mat((np.random.rand(self.itemNum, self.latentFactorNum)-0.05)*0.01)
# self.bu = [0.0 for i in range(self.userNum)]
# self.bi = [0.0 for i in range(self.itemNum)]
# temp = math.sqrt(self.latentFactorNum)
# self.U = [[(0.1 * random.random() / temp) for i in range(self.latentFactorNum)] for j in range(self.userNum)]
# self.V = [[0.1 * random.random() / temp for i in range(self.latentFactorNum)] for j in range(self.itemNum)]
print("Initialize end.The user number is:%d,item number is:%d" % (self.userNum, self.itemNum))
def train(self, iterTimes=100):
print("Beginning to train the model......")
preRmse = 10000.0
temp_count = 0
for iter in range(iterTimes):
count=0
for index in self.ua_base_explict.index:
user = int(self.ua_base_explict.loc[index]['user_id'])-1
item = int(self.ua_base_explict.loc[index]['item_id'])-1
rating = float(self.ua_base_explict.loc[index]['rating'])
pscore = self.predictScore(self.mu, self.bu[user], self.bi[item], self.U[user], self.V[item],self.W[item],user+1)
eui = rating - pscore
# update parameters bu and bi(user rating bais and item rating bais)
self.mu= -eui
self.bu[user] += self.learningRate * (eui - self.beta_u * self.bu[user])
self.bi[item] += self.learningRate * (eui - self.beta_v * self.bi[item])
temp_Uuser = self.U[user]
temp_Vitem = self.V[item]
if user+1 in self.implict.index:
temp = self.implict.loc[user+1][self.implict.loc[user+1].isnull() == False]
U_bar = self.W[temp.index-1].sum()/temp.count()
else:
U_bar = np.zeros(self.latentFactorNum)
self.U[user] += self.learningRate * (eui * self.V[user] - self.alpha_u * self.U[user])
self.V[item] += self.learningRate * ((temp_Uuser+U_bar) * eui - self.alpha_v * self.V[item])
if user+1 in self.implict.index:
self.W[item] += self.learningRate * (eui * temp_Vitem / math.sqrt(self.implict.loc[user+1].count())- self.alpha_w * self.W[item])
else:
self.W[item] += self.learningRate * (eui * temp_Vitem - self.alpha_w * self.W[item])
# for k in range(self.latentFactorNum):
# temp = self.U[user][k]
# # update U,V
# self.U[user][k] += self.learningRate * (eui * self.V[user][k] - self.alpha_u * self.U[user][k])
# self.V[item][k] += self.learningRate * (temp * eui - self.alpha_v * self.V[item][k])
#
count += 1
if count % 5000 == 0 :
print("第%s轮进度：%s/%s" %(iter+1,count,len(self.ua_base_explict.index)))
# calculate the current rmse
self.learningRate = self.learningRate * 0.9 # 缩减学习率
curRmse = self.test()
print("Iteration %d times,RMSE is : %f" % (iter + 1, curRmse))
if curRmse > preRmse:
break
else:
preRmse = curRmse
print("Iteration finished!")
# test on the test set and calculate the RMSE
def test(self):
cnt = self.test_df.shape[0]
rmse = 0.0
# buT=bu.reshape(bu.shape[0],1)
# predict_rate_matrix = mu + np.tile(buT,(1,self.itemNum))+ np.tile(bi,(self.userNum,1)) + self.U * self.V.T
cur = 0
for i in self.test_df.index:
cur +=1
if cur % 1000 == 0:
print("测试进度:%s/%s" %(cur,len(self.test_df.index)))
user = int(self.test_df.loc[i]['user_id']) - 1
item = int(self.test_df.loc[i]['item_id']) - 1
score = float(self.test_df.loc[i]['rating'])
pscore = self.predictScore(self.mu,self.bu[user], self.bi[item], self.U[user], self.V[item],self.W[item],user+1)
# pscore = predict_rate_matrix[user,item]
rmse += math.pow(score - pscore, 2)
#print(score,pscore,rmse)
RMSE=math.sqrt(rmse / cnt)
return RMSE
# calculate the inner product of two vectors
def innerProduct(self, v1, v2):
result = 0.0
for i in range(len(v1)):
result += v1[i] * v2[i]
return result
def predictScore(self, mu, bu, bi, U, V, W ,user_id):
#pscore = mu + bu + bi + self.innerProduct(U, V)
if user_id in self.implict.index:
temp = self.implict.loc[user_id][self.implict.loc[user_id].isnull() == False]
U_bar = self.W[temp.index-1].sum() / temp.count()
else:
U_bar = np.zeros(self.latentFactorNum)
pscore = mu + bu + bi + np.multiply(U,V).sum() +np.multiply(U_bar,V).sum()
if np.isnan(pscore):
print("!!!!")
print(mu,bu,bi,np.multiply(U,V).sum(),np.multiply(U_bar,V).sum(),U_bar)
if pscore < 1:
pscore = 1
if pscore > 5:
pscore = 5
return pscore
if __name__ == '__main__':
s = SVDplusplus("../datasets/ml-100k/u.data", "../datasets/ml-100k/u1.base", "../datasets/ml-100k/u1.test")
s.train()