Information Technology Reference
In-Depth Information
simultaneously modeled the
tag
-
tag
,
image
-
image
and
image
-
tag
relationships, they
aggregated images' tags over all users, thereby losing important information about
individual user's variation in tag usage. In this chapter, we exploit the social aspect
of the photo sharing websites and consider
user
factor into the tag refinement prob-
lem. We believe that incorporation of
user
information will facilitate explaining the
tagging data and lead to better estimates of image and tag factors.
2.3 Methods for Social Image Tag Refinement
The low dimensional
user
,
image
and
tag
factor matrices can be viewed as compact
representations in the corresponding latent subspaces. The latent subspaces capture
the relevant attributes, e.g., the user dimensions are related to users' preferences or
social interests, the image dimensions indicate visual themes and the tag dimensions
are related to the semantic topics of tags. The basic intuition behind this work is:
The
incorporation of
user
information will help extract more compact and informative
image
and
tag
representations in the semantic subspaces. The task of image tag
refinement is then solved by computing the cross-space
image
-
tag
associations.
In
this section we first introduce the idea of jointly modeling the
user
,
image
and
tag
factors into a tensor factorization framework, then explain how to employ the derived
factors for tag refinement.
In the following, we denote tensors by calligraphic uppercase letters (e.g.,
Y
),
,
,
matrices by uppercase letters (e.g.,
U
I
T
), vectors by bold lowercase letters (e.g.,
,
,
u
i
), scalars by lowercase letters (e.g.,
u
i
) and sets by blackboard bold letters (e.g.,
U
,
I
,
T
).
Tensor Factorization.
There are three types of entities in the photo sharing web-
sites. The tagging data can be viewed as a set of triplets. Let
denote the sets of
users, images, tags and the set of observed tagging data is denoted by
U
,
I
,
T
O ↂ U×I×T
,
i.e., each triplet
means that user
u
has annotated image
i
with tag
t
.
The ternary interrelations can be viewed as a three-mode cube, where the modes
are the
user
,
image
and
tag
. Therefore, we can induce a three dimensional tensor
Y
∈ R
|
U
|×|
I
|×|
T
|
, which is defined as:
(
u
,
i
,
t
)
∈ O
1f
)
∈ O
0 otherwise
(
u
,
i
,
t
y
u
,
i
,
t
=
(2.1)
where
are the number of distinct users, images and tags respectively.
To jointly model the three factors of
user
,
image
and
tag
, we employ the general
tensor factorization model, Tucker Decomposition for the latent factor inference. In
Tucker Decomposition, the tagging data
|U|
,
|I|
,
|T|
Y
are estimated by three low-rank matrices
and one core tensor:
Y
:=
C
×
u
U
×
i
I
×
t
T
(2.2)
