7.3. PCW-DC 83
7.3 PCW-DC
is section details the proposed PCW-DC. We first formulate the research problem and then
detail the two key components of the scoring model: user modeling and garment modeling,
based on which we can perform the PCW creation.
7.3.1 PROBLEM FORMULATION
In this work, to be cost-friendly, we focus on creating a PCW based on the user’s original
wardrobe (i.e., the set of historical purchased fashion items). Let I
u
D fi
u
ck
j c D1; : : : ; C I k D
1; : : : ; N
c
g be the original wardrobe of the user u, comprising a set of fashion items from C cat-
egories (e.g., the top, bottom and outer), where N
c
denotes the total number of items belonging
to the category c. In addition, we have a set of items I D fi
n
g
N
nD1
, and each item i
n
is associated
with a visual image and a textual description. Our task is to generate a new personalized capsule
wardrobe
e
I
u
for the user u based on I
u
and I that provides the user both compatible and suit-
able outfits. In a sense, we should get rid of inappropriate items from I
u
and add proper items
from I to maximize the user-garment and garment-garment compatibilities of the wardrobe.
Essentially, we aim to propose a comprehensive wardrobe compatibility scoring model
S./, based on which we can perform the PCW creation. In particular, we define S./ as follows:
S
I
D ˛U
I
j‚
U
C .1 ˛/G
I
j‚
G
; (7.1)
where I
represents a candidate wardrobe. U and G denote the compatibility modeling from
the user-garment and garment-garment perspectives, respectively. ˛ is a trade-off parameter to
balance the evaluation score of each component. ‚
U
and ‚
G
refer to the to-be-learned model
parameters of the user modeling and garment modeling, respectively.
User Preference Modeling
Intuitively, it is reasonable to argue that different individuals may prefer different item appear-
ances and categories. For example, some people may prefer the white top instead of a black one,
while others prefer the skirt rather than the short. In fact, user preference modeling in fashion
domain has been studied by recent work [34], whereby two latent spaces are introduced to mea-
sure the user’s overall preference and visual preference for a given item, respectively. However,
this method overlooks the value of the item’s textual context in the user preference modeling.
In fact, the textual description, including the item title and category metadata, can summarize
the key semantic features of items, like the style, material and category, and hence deliver im-
portant cues of the user preferences. erefore, in this work, to comprehensively model the user
preferences, we formulate x
p
ui
as follows:
x
p
ui
D
T
u
i
C
T
u
W
p
Œ
f
i
; t
i
C ˇ
p
; (7.2)
where
u
2 R
K
and
i
2 R
K
are latent factors of the user u and the item i, respectively.
u
2 R
D
is the latent content factor of the user u. Œf
i
; t
i
refers to the concatenation of item visual feature
84 7. PERSONALIZED CAPSULE WARDROBE CREATION
f
i
and textual feature t
i
. W
p
and ˇ
p
are parameters of the nonlinear operation that maps the
item features to the latent preference space. e first and second term of the equation encode
the overall preference and content preference of the user u toward the item i, respectively.
For the optimization of the user preference modeling, we adopt the BPR network, which
has been proven to be an effective optimization framework for the pairwise preference rank-
ing [108]. Based on BPR, we build the following training set D
s
D f.u; i; j /g, where i 2 I
u
and j 2 I n I
u
. Each triplet .u; i; j / indicates that the user u prefers the item i to the item j .
en according to [100], we have the following objective function:
arg min
‚
U
X
.u;i;j /2D
s
ln
x
p
ui
x
p
uj
: (7.3)
User Body Shape Modeling
As aforementioned, people with different body shapes would go with different types of items.
As such, we assume that there should be a latent space where the compatibility between body
shapes and item contents can be well captured. We first obtain the body shape for each user
based on our body shape assignment scheme, which will be detailed in Section 4.2. Due to the
fact that each user can be assigned with only one body shape, we represent each user with an
one-hot encoding u
s
2 R
Q
, where Q is the total number of possible body shapes. And then, we
attempt to learn the item embedding toward the body shape compatibility modeling.
On the one hand, the matching knowledge between items and body shapes can be explic-
itly affected by the item appearance. We thus employ the MLP to map the item content to the
body shape matching space. In particular, the item embedding i
s
2 R
Q
, derived from its visual
and textual features, can be designed as follows:
i
s
D
.
W
s
Œ
f
i
; t
i
C ˇ
s
/
; (7.4)
where Œf
i
; t
i
is same as that in Eq. (7.2). W
s
and ˇ
s
are the parameters of the MLP. .x/ D
1
1Cexp.x/
is the nonlinear activation function.
On the other hand, the matching knowledge can be implicitly conveyed by the user’s his-
torical reviews on their purchased items, as users tend to purchase items that highlight their
figure strength and hide the shortcomings. Accordingly, we define the item referenced embed-
ding i
s
2 R
Q
as follows:
i
s
D softmax
0
@
X
u2U
i
u
s
1
A
; (7.5)
where U
i
denotes the set of users who bought the item i. softmax.x/ D
exp.x
i
/
P
K
kD1
exp.x
k
/
is a nor-
malized exponential function. Ultimately, we argue that the matching knowledge obtained from
item contents and the historical reviews should be consistent, that is, the item embedding i
s
and
item referenced embedding i
s
should be close. Consequently, we reach the following objective
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