\min BPR\_OPT + \frac{\lambda_f}{2}\sum\limits_{i,j}^{I} \|q_i-q_j\|^2 \cdot W_{ij}
min
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f
2
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i
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I
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W
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\min BPR\_OPT + \frac{\lambda_f}{2}\sum\limits_{i,j}^{I} \|q_i-q_j\|^2 \cdot W_{ij}
min
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O
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2
λ
f
i
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j
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I
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W
i
j
\min BPR\_OPT +\frac{\lambda_m}{2}\sum\limits_{i}^{I}\sum\limits_{j}^{I}\sum\limits_{c}^{C}\|q_i-q_j\|^2 \cdot W_{ijc}
min
B
P
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O
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m
2
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I
∑
j
I
∑
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C
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q
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2
⋅
W
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j
c
\min BPR\_OPT +\frac{\lambda_m}{2}\sum\limits_{i}^{I}\sum\limits_{j}^{I}\sum\limits_{c}^{C}\|q_i-q_j\|^2 \cdot W_{ijc}
min
B
P
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λ
m
i
∑
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j
∑
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c
∑
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⋅
W
i
j
c
W_{ijc} = \begin{cases} A_{ic} \cdot A_{jc} \cdot sim(f_{ic},\ f_{jc}) & both\ i,\ j \in co \_cluster\ c \\ 0 & else \end{cases}
W
i
j
c
=
{
A
i
c
⋅
A
j
c
⋅
s
i
m
(
f
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c
,
f
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)
b
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∈
c
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c
l
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s
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e
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c
0
e
l
s
e
W_{ijc} = \begin{cases} A_{ic} \cdot A_{jc} \cdot sim(f_{ic},\ f_{jc}) & both\ i,\ j \in co \_cluster\ c \\ 0 & else \end{cases}
W
i
j
c
=
{
A
i
c
⋅
A
j
c
⋅
s
i
m
(
f
i
c
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0
b
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t
h
i
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∈
c
o
_
c
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u
s
t
e
r
c
e
l
s
e
W_{ijc} = \begin{cases} sim(f_{ic},\ f_{jc}) & both\ i,\ j \in co \_cluster\ c \\ 0 & else \end{cases}
W
i
j
c
=
{
s
i
m
(
f
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c
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c
)
b
o
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∈
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c
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c
0
e
l
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e
W_{ijc} = \begin{cases} sim(f_{ic},\ f_{jc}) & both\ i,\ j \in co \_cluster\ c \\ 0 & else \end{cases}
W
i
j
c
=
{
s
i
m
(
f
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c
,
f
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c
)
0
b
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\frac{\partial F}{\partial V_j} = Y_{ij}[g(-f_{ij})+\sum\limits_{k=1}^{N}\frac{Y_{ik}g'(f_{ik}-f_{ij})}{1-Y_{ik}g(f_{ik}-f_{ij})}]U_i-\lambda V_j
∂
F
∂
V
j
=
Y
i
j
[
g
(
−
f
i
j
)
+
∑
k
=
1
N
Y
i
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g
′
(
f
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−
f
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j
)
1
−
Y
i
k
g
(
f
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k
−
f
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j
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]
U
i
−
λ
V
j
\frac{\partial F}{\partial V_j} = Y_{ij}[g(-f_{ij})+\sum\limits_{k=1}^{N}\frac{Y_{ik}g'(f_{ik}-f_{ij})}{1-Y_{ik}g(f_{ik}-f_{ij})}]U_i-\lambda V_j
∂
V
j
∂
F
=
Y
i
j
[
g
(
−
f
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+
k
=
1
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N
1
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Y
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i
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)
Y
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k
g
′
(
f
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k
−
f
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j
)
]
U
i
−
λ
V
j
\min BPR\_OPT + \frac{\lambda_f}{2}\sum\limits_{i,j}^{I} \|q_i-q_j\|^2 \cdot \textbf{W}_{ij}
min
B
P
R
_
O
P
T
+
λ
f
2
∑
i
,
j
I
∥
q
i
−
q
j
∥
2
⋅
W
i
j
\min BPR\_OPT + \frac{\lambda_f}{2}\sum\limits_{i,j}^{I} \|q_i-q_j\|^2 \cdot \textbf{W}_{ij}
min
B
P
R
_
O
P
T
+
2
λ
f
i
,
j
∑
I
∥
q
i
−
q
j
∥
2
⋅
W
i
j
\frac{\partial F}{\partial V_j} = Y_{ij}[g(-f_{ij})+\sum\limits_{k=1}^{N}Y_{ik}g'(f_{ij}-f_{ik})(\frac{1}{1-Y_{ik}g(f_{ik}-f_{ij})}-\frac{1}{1-Y_{ij}g(f_{ij}-f_{ik})})U_i]-\lambda V_j
∂
F
∂
V
j
=
Y
i
j
[
g
(
−
f
i
j
)
+
∑
k
=
1
N
Y
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g
′
(
f
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k
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(
1
1
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Y
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g
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)
−
1
1
−
Y
i
j
g
(
f
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j
−
f
i
k
)
)
U
i
]
−
λ
V
j
\frac{\partial F}{\partial V_j} = Y_{ij}[g(-f_{ij})+\sum\limits_{k=1}^{N}Y_{ik}g'(f_{ij}-f_{ik})(\frac{1}{1-Y_{ik}g(f_{ik}-f_{ij})}-\frac{1}{1-Y_{ij}g(f_{ij}-f_{ik})})U_i]-\lambda V_j
∂
V
j
∂
F
=
Y
i
j
[
g
(
−
f
i
j
)
+
k
=
1
∑
N
Y
i
k
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′
(
f
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(
1
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Y
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1
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1
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1
)
U
i
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−
λ
V
j
\epsilon(A,B)=\sum\limits_{u=1}^{U}\sum\limits_{i=1}^{I}{\|\frac{A_u}{\sqrt{D_{uu}} - \frac{B_i}{\sqrt{D_{ii}}}\|}^2
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