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v
T
×|
V
|
1
; (2) Node topic distribution
T
×
1
for each user
u
; and (3)
ʦ
ↂ R
ʩ
u
ↂ R
and
)
ↂ R
|
U
|×|
U
|
,
t
.
2
ʨ(
={
,
···
,
}
Topic-sensitive edge strength
t
1
T
We propose a probabilistic generative model for topic-sensitive influencer mining.
Since the model specifies the generation process of the visual image content as well
as the textual tag words for each user, we call it multimodal topic-sensitive influence
model (mmTIM).
4.3.1 Data Justification and Assumption
We consider the influence modeling problem from a generative perspective. It is well
recognized that users' online activity is impacted a lot by their influencers [
1
,
25
].
The uploaded images and annotated tags can be viewed as observations of users'
activities. Therefore, our solution begins with using the observed user activity data
to infer the desired social influence structure.
To design the generation process, we conduct data analysis to support our assump-
tion, by tracking user interest change over time. Flickr user data at two timestamps,
t
0
:
March 3rd, 2011 and
t
1
:
Sept. 3rd, 2011 are crawled. We select 500 pairs of users
{
on condition that at time
t
0
,user
B
is not in the contact list of user
A
while at
time
t
1
,user
B
has been added contact user by user
A
. Multimodal topic modeling [
3
]
is conducted using data at both timestamps, with user corresponding to document
and user activity corresponding to word. We obtain the topic distribution for each
user and calculate user interest similarity by the symmetric KL-divergence between
each pair of users
A
,
B
}
. The user interest similarity distribution at two timestamps
is illustrated in Fig.
4.1
a and b, respectively. The user interest similarity scores at
time
t
0
cluster below 0
{
A
,
B
}
15, while at time
t
1
the scores distribute more scatteredly. To
highlight the change, we visualize the quotient in Fig.
4.1
c, where quotient value of
larger than 1 indicates user interest becoming more close after adding contact user. It
is obvious that most quotient values are above the red line, from which we conclude
that user
A
's activity and interest are influenced by the contact user.
Inspired by this, for each user, we assume that his/her tag words and uploaded
images are generated in two ways, either
innovative
—mainly depending on his/her
own interest or
influenced
—being more influenced by the influencers. For example,
when Bob uploads an image, the theme of the image may match his own original
interest, or follow one of his influencers. Another example, the tag Bob chooses for
annotation can be viewed as either originally generated or borrowed from his contact
users.
.
1
We use topic distributions over tag words and visual descriptors to represent the topic space:
T
is
the number of topics,
|
W
|
is the size of tag vocabulary, and
|
V
|
is the size of visual-descriptor
vocabulary.
2
ʨ
(
t
),
u
2
∈
C
u
1
measures the influence strength from user
u
2
to
u
1
in the
t
th topic.
u
1
,
u
2
