52 5. PROTOTYPE-WISE INTERPRETABLE COMPATIBILITY MODELING
learning,
L
nmf
D
G
p
PH
p
2
F
C
G
u
UH
u
2
F
: (5.8)
It is intuitive that the top and bottom of one compatible prototype should be more com-
patible than those of the incompatible ones. erefore, we define the intrinsic compatibility for
each prototype p
l
(u
r
) as follows:
s
p
l
D
Qp
t
l
T
Qp
b
l
; s
u
r
D
Qu
t
r
T
Qu
b
r
; (5.9)
where s
p
l
and s
u
r
are the intrinsic compatibility for the compatible prototype p
l
and incompatible
prototype u
r
, respectively. Qp
t
l
, Qp
b
l
, Qu
t
r
, and Qu
b
r
are the hidden representations of p
t
l
, p
b
l
, u
t
r
, and
u
b
r
, respectively, which can be acquired based on Eq. (5.2).
To seamlessly integrate the latent prototype learning and compatible modeling, for each
sample .i; j; k/, we particularly define its most similar compatible and incompatible prototypes
p
l
and u
r
with the Euclidean distance, whose indexes l
and r
can be derived as follows:
8
ˆ
ˆ
<
ˆ
ˆ
:
d
p
.i; j; l/ D
f
t
i
f
b
j
p
t
l
p
b
l
2
; d
u
.i; k; r/ D
f
t
i
f
b
k
u
t
r
u
b
r
2
;
l
D arg min
l
d
p
.i; j; l/ ; r
D arg min
r
d
u
.i; k; r/:
(5.10)
In a sense, we expect that the intrinsic compatibility of the compatible prototype p
l
should be
higher than that of the incompatible one u
r
. erefore according to the BPR, we thus have the
following adaptive objective function:
L
proto
bpr
D
X
.i;j;k/2D
S
ln
s
p
l
s
u
r
;
(5.11)
where s
p
l
and s
u
r
can be obtained with Eq. (5.9). Interestingly, with L
item
bpr
and L
proto
bpr
, the com-
patibility modeling between fashion items and the prototype learning can be mutually promoted.
Ultimately, we obtain the final objective function as follows:
L D L
item
bpr
C L
proto
bpr
C L
nmf
;
(5.12)
where and are the non-negative trade-off hyperparameters to weigh the different compo-
nents of the objective function.
5.3.5 INTERPRETABLE ATTRIBUTE MANIPULATION
In order to transform the incompatible fashion item pairs into the compatible ones, we first
employ the L
p
compatible prototypes as templates to identify the discordant attributes. In par-
ticular, for the given negative (incompatible) top-bottom pair .t
i
; b
k
/, we particularly find the