3.3. METHODOLOGY 17
3.3.5 BPR-DAE
In a sense, we can easily identify the positive top-bottom pairs as which have been paired within
the same outfits by fashion experts. Regarding the non-paired items (e.g., top-bottom pairs),
they may just indicate the incompatibility between pairs or the missing potential positive pairs
(i.e., pairs may be created in the future). erefore, to fully take advantage of these implicit
relationship between tops and bottoms, we naturally adopt the BPR framework. We assume
that bottoms from the positive set B
C
i
are more favorable to top t
i
than those unobserved neutral
bottoms. According to BPR, we build a training set:
D
S
WD
˚
.i; j; k/jt
i
2 T ; b
j
2 B
C
i
^ b
k
2 BnB
C
i
; (3.5)
where the triple .i; j; k/ indicates that bottom b
j
is more compatible than bottom b
k
with top
t
i
.
en according to [100], we have the following objective function,
L
bpr
D
X
.i;j;k/2D
S
ln
m
ijk
; (3.6)
where m
ijk
WD m
ij
m
ik
, capturing the compatibility preference between top t
i
, bottom b
j
com-
pared to bottom b
k
, and the is the sigmoid function. In addition, according to Eq. (3.4) and
taking the modality consistency into consideration, we have
L
mod
D
X
.i;j;k/2D
S
L
mod
Qv
t
i
; Qc
t
i
C L
mod
Qv
b
j
; Qc
b
j
C L
mod
Qv
b
k
; Qc
b
k
: (3.7)
Finally, we have the following objective function:
L D L
bpr
C L
mod
C L
rec
C
2
‚
2
F
; (3.8)
where L
rec
D L
v
rec
C L
c
rec
, L
v
rec
D
P
.i;j;k/2D
S
l.v
t
i
/ C l. v
b
j
/ C l. v
b
k
/
, and L
c
rec
D
P
.i;j;k/2D
S
l.c
t
i
/ C l. c
b
j
/ C l.c
b
k
/
. , , are the nonnegative trade-off hyperparame-
ters, and ‚ refers to the set of parameters (i.e., W
k
and
O
W
k
). e last regularizer term is
designed to avoid overfitting.
3.3.6 OPTIMIZATION
Toward the optimization, the core step is to calculate the partial derivative with respect to pa-
rameters @L=@W
xy
k
and @L=@
O
W
xy
k
, x 2 ft; bg, y 2 fv; cg. Due to the space limitation, we here
only introduce the detailed calculation for
@
L
=@
W
tv
k
, @L=@
O
W
tv
k
, while the other partial derivative
can be solved in similar fashion.
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