3.3. NETWORK-BASED DETECTION 45
     u
i
       
   E 2 f0; 1g
mN
 E
ij
D 1    u
i
   
      a
j
 E
ij
D 0
           
   x
i
          
         x
i
       
          x
i
   

Q
x
i
           x
i
; i D 1; :::; m 
   
Q
x
1
;
Q
x
2
; :::;
Q
x
m
     i    
 h
i1
    
Q
x
i
       h
i
  
h
i
          i     
       h
m
        
     a
j
D tanh.Wh
m
C b/ b      
 a
j
        
Embedding Layer
h
x̃
x̃
i
x̃
m
...
h
i
x
i
x
...
h
m
W a
j
x
m
         
3.3.4 INTERACTION NETWORK MODELING
           
                
             
             
             
        
       
            
            
            
             
          
46 3. HOW SOCIAL CONTEXT HELPS
News
Content
Embedding
User
Embedding
Linear
Classifie
User-News
Interaction
Embedding
Publisher-News
Relation
Embedding
d
m k
k
k
k
k
n
k
m
m
m + r
nr
nr
m + r
r
r
N = N
× k
×
m
= m
=
= p
l
= r
× n
× k
× k
× k
× k
× k
k d
X
A U
U
o
FB
× k
F
L
F
U
y
U
p
q
F
L
p
y
L
L
T U
T
U
T
F
T
F V
T
Interaction Network
Tri-Relationship Embedding Fake News Prediction
L
B W A
p
p
a
a
a
u
u
u
u
           
           
         
News Embedding             
                
            
              
   F
User Embedding          
             
              
            
           
  A 2 f0; 1g
mm
    U 2 R
mk
C
   
  
min
U;T0
kY ˇ .A UTU
T
/k
2
F
;

 U      T 2 R
kk
C
      Y 2 R
mm
    A        A     Y D
3.3. NETWORK-BASED DETECTION 47
sign.A/            
    
User-News Embedding          
        
y
Lj
   
               
                
      s D fs
1
; s
2
; :::; s
m
g       
 s
i
2 Œ0; 1    u
i
       
  E 2 f0; 1g
mN
 E
ij
D 1    u
i
    
     a
j
 E
ij
D 0       
min
m
X
iD1
r
X
j D1
E
ij
s
i
1
1 C y
Lj
2
jjU
i
F
j
jj
2
2
ƒ‚
 
C
m
X
iD1
r
X
j D1
E
ij
.1 s
i
/
1 C y
Lj
2
jjU
i
F
j
jj
2
2
ƒ‚
 
;

 y
L
2 R
r1
            
      y
Lj
D 1        
                 y
Lj
D 1
              
     
Publisher-News Embedding       
               
              
               
              
            o 
    o 2 R
l1
   B 2 R
lN
  
     
min k
N
BFQ ok
2
2
;

                
  
N
BD
N
B        
N
B
kj
D
B
kj
P
n
j D1
B
kj
Q 2 R
k1
         
     o
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