徐志远

推荐算法工程师的学习日常

0%

Neural Graph Collaborate Filtering

接下来一段时间可能会主要关注图学习在推荐系统中的运用。先来一篇何老师的NGCF。

论文背景

传统的协同过滤主要学习两点。

  1. 学习物品和用户的表示。
  2. 学习物品和用户的交互。
    但是它们都缺乏显式的协同信号。解决这两个问题的办法就是探究高阶的连接交互。虽然近期Hop-Rec也提出类似的概念,但是仅仅丰富了训练数据,最后交互依然用的MF。所以它们是本质不同的。

模型结构

模型结构比较容易。

user embeddings and item embeddings

模型结构图

First order propagation

$ m_{u \leftarrow i} = f(e_i,e_u,p_{ui}) $

其中文中给的$ f $:

$ m_{u \leftarrow i} = \frac{1}{\sqrt(|N_u| )\sqrt(|N_i| )}(W_1e_i+W_2(e_i \odot e_u)) $

Message Aggregation

$ e_u^{(1)} = LeakyRelu(m_{u \leftarrow u} + \Sigma_{i \in N_u} m_{u \leftarrow i}) $

Higher order propagation

和First order propagation类似

Model prediction

$ y_{NGCF}(u,i) = e_u ^T e_i $

Optimization

$ Loss = \Sigma_{(u,i,j) \in O } -ln \sigma(\hat{y_{u,i}} - \hat{y_{u,j}} ) + \lambda || \theta||^2_2 $

Model size

用了很少的额外空间就达到了高阶的连接。

Message and Node dropout

node dropout能够提高泛化能力。

实验效果

总的来看,实验结果还是挺不错的。但是依据历史发展规律来看,还有很多可以改进。不然也不会出lightgcn了哈哈。

代码

Github

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
import torch
import torch.nn as nn
from torch.nn import Module
from scipy.sparse import coo_matrix
from scipy.sparse import vstack
from scipy import sparse
import numpy as np


class SVD(Module):

def __init__(self,userNum,itemNum,dim):
super(SVD, self).__init__()
self.uEmbd = nn.Embedding(userNum,dim)
self.iEmbd = nn.Embedding(itemNum,dim)
self.uBias = nn.Embedding(userNum,1)
self.iBias = nn.Embedding(itemNum,1)
self.overAllBias = nn.Parameter(torch.Tensor([0]))

def forward(self, userIdx,itemIdx):
uembd = self.uEmbd(userIdx)
iembd = self.iEmbd(itemIdx)
ubias = self.uBias(userIdx)
ibias = self.iBias(itemIdx)

biases = ubias + ibias + self.overAllBias
prediction = torch.sum(torch.mul(uembd,iembd),dim=1) + biases.flatten()

return prediction

class NCF(Module):

def __init__(self,userNum,itemNum,dim,layers=[128,64,32,8]):
super(NCF, self).__init__()
self.uEmbd = nn.Embedding(userNum,dim)
self.iEmbd = nn.Embedding(itemNum,dim)
self.fc_layers = torch.nn.ModuleList()
self.finalLayer = torch.nn.Linear(layers[-1],1)

for From,To in zip(layers[:-1],layers[1:]):
self.fc_layers.append(nn.Linear(From,To))

def forward(self, userIdx,itemIdx):
uembd = self.uEmbd(userIdx)
iembd = self.iEmbd(itemIdx)
embd = torch.cat([uembd, iembd], dim=1)
x = embd
for l in self.fc_layers:
x = l(x)
x = nn.ReLU()(x)

prediction = self.finalLayer(x)
return prediction.flatten()


class GNNLayer(Module):

def __init__(self,inF,outF):

super(GNNLayer,self).__init__()
self.inF = inF
self.outF = outF
self.linear = torch.nn.Linear(in_features=inF,out_features=outF)
self.interActTransform = torch.nn.Linear(in_features=inF,out_features=outF)

def forward(self, laplacianMat,selfLoop,features):
# for GCF ajdMat is a (N+M) by (N+M) mat
# laplacianMat L = D^-1(A)D^-1 # 拉普拉斯矩阵
L1 = laplacianMat + selfLoop
L2 = laplacianMat.cuda()
L1 = L1.cuda()
inter_feature = torch.sparse.mm(L2,features)
inter_feature = torch.mul(inter_feature,features)

inter_part1 = self.linear(torch.sparse.mm(L1,features))
inter_part2 = self.interActTransform(torch.sparse.mm(L2,inter_feature))

return inter_part1+inter_part2

class GCF(Module):

def __init__(self,userNum,itemNum,rt,embedSize=100,layers=[100,80,50],useCuda=True):

super(GCF,self).__init__()
self.useCuda = useCuda
self.userNum = userNum
self.itemNum = itemNum
self.uEmbd = nn.Embedding(userNum,embedSize)
self.iEmbd = nn.Embedding(itemNum,embedSize)
self.GNNlayers = torch.nn.ModuleList()
self.LaplacianMat = self.buildLaplacianMat(rt) # sparse format
self.leakyRelu = nn.LeakyReLU()
self.selfLoop = self.getSparseEye(self.userNum+self.itemNum)

self.transForm1 = nn.Linear(in_features=layers[-1]*(len(layers))*2,out_features=64)
self.transForm2 = nn.Linear(in_features=64,out_features=32)
self.transForm3 = nn.Linear(in_features=32,out_features=1)

for From,To in zip(layers[:-1],layers[1:]):
self.GNNlayers.append(GNNLayer(From,To))

def getSparseEye(self,num):
i = torch.LongTensor([[k for k in range(0,num)],[j for j in range(0,num)]])
val = torch.FloatTensor([1]*num)
return torch.sparse.FloatTensor(i,val)

def buildLaplacianMat(self,rt):

rt_item = rt['itemId'] + self.userNum
uiMat = coo_matrix((rt['rating'], (rt['userId'], rt['itemId'])))

uiMat_upperPart = coo_matrix((rt['rating'], (rt['userId'], rt_item)))
uiMat = uiMat.transpose()
uiMat.resize((self.itemNum, self.userNum + self.itemNum))

A = sparse.vstack([uiMat_upperPart,uiMat])
selfLoop = sparse.eye(self.userNum+self.itemNum)
sumArr = (A>0).sum(axis=1)
diag = list(np.array(sumArr.flatten())[0])
diag = np.power(diag,-0.5)
D = sparse.diags(diag)
L = D * A * D
L = sparse.coo_matrix(L)
row = L.row
col = L.col
i = torch.LongTensor([row,col])
data = torch.FloatTensor(L.data)
SparseL = torch.sparse.FloatTensor(i,data)
return SparseL

def getFeatureMat(self):
uidx = torch.LongTensor([i for i in range(self.userNum)])
iidx = torch.LongTensor([i for i in range(self.itemNum)])
if self.useCuda == True:
uidx = uidx.cuda()
iidx = iidx.cuda()

userEmbd = self.uEmbd(uidx)
itemEmbd = self.iEmbd(iidx)
features = torch.cat([userEmbd,itemEmbd],dim=0)
return features

def forward(self,userIdx,itemIdx):

itemIdx = itemIdx + self.userNum
userIdx = list(userIdx.cpu().data)
itemIdx = list(itemIdx.cpu().data)
# gcf data propagation
features = self.getFeatureMat()
finalEmbd = features.clone()
for gnn in self.GNNlayers:
features = gnn(self.LaplacianMat,self.selfLoop,features)
features = nn.ReLU()(features)
finalEmbd = torch.cat([finalEmbd,features.clone()],dim=1)

userEmbd = finalEmbd[userIdx]
itemEmbd = finalEmbd[itemIdx]
embd = torch.cat([userEmbd,itemEmbd],dim=1)

embd = nn.ReLU()(self.transForm1(embd))
embd = self.transForm2(embd)
embd = self.transForm3(embd)
prediction = embd.flatten()

return prediction