Information Technology Reference
In-Depth Information
Fig. 4.4
Generative process of query
q
and image
d
in personalized image search. Reference
[
26
]
c
2012 Association for Computing Machinery, Inc. Reprinted by permission
u
v
u
w
depends on [
ʸ
Q
,ʸ
D
] and [
ʸ
Q
,ʸ
D
], respectively. User
u
generates the query
q
by first
u
selecting
q
and then choosing a query from the selected model. Similar hierarchical
process happens to image visual content
v
d
and textual annotation
w
d
. Therefore, the
generative process in Fig.
4.4
can be summarized by:
u
ʸ
u
v
ₒ
ʸ
Q
ₒ
q
,
V
ₒ
ʸ
D
ₒ
v
D
w
and
w
D
.
We consider the task of personalized image search as returning a list of images to
the issued query
q
according to preference of searcher
u
. In the context of Bayesian
decision theory, to each action, there is an associated loss
L
, which, in our case,
is the loss for returning an individual image to the searcher. Under this frame-
work, the expected risk of returning individual image
d
is decomposed into two
components:
W
ₒ
ʸ
D
ₒ
R
(
q
,
u
,
d
)
=
μ
R
(
q
,
u
,
v
d
)
+
(
1
−
μ)
R
(
q
,
u
,
w
d
)
p
r
D
u
v
u
v
=
μ
p
(ʸ
Q
|
q
,
u
)
p
(ʸ
D
|
v
d
)
(
q
,
u
,
v
d
)
|
ʸ
Q
,ʸ
Q
D
L
ʸ
v
d
)
d
u
v
v
u
Q
×
Q
,ʸ
D
,
r
(
q
,
u
,
ʸ
D
d
ʸ
p
r
D
u
w
u
w
+
(
1
−
μ)
p
(ʸ
Q
|
q
,
u
)
p
(ʸ
D
|
w
d
)
(
q
,
u
,
w
d
)
|
ʸ
Q
,ʸ
Q
D
L
ʸ
w
d
)
d
u
w
w
u
Q
×
Q
,ʸ
D
,
r
(
q
,
u
,
ʸ
D
d
ʸ
(4.9)
where
μ
is weight parameter controlling the strength of visual content and tag words,
u
is the probability of generating relevance
r
given the query and image
model parameters
p
(
r
|
ʸ
Q
,ʸ
D
)
u
Q
ʸ
D
. Following the derivation operation from [
14
], we
consider the case that the loss function
L
depends only on model parameters
ʸ
and
u
Q
ʸ
and
ʸ
D
. Formally, let
L
be proportional to a distance measure
ʔ(
·
)
between model
parameters, i.e.,
L
ʸ
r
∝
ʔ(ʸ
u
u
Q
,ʸ
D
,
Q
,ʸ
D
)
