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combined-relational network—which is integrated with multiple networks extracted
from the web—to learn and predict the ranking. The important question that must
be resolved here is
how to combine relations to describe a given ranking best
.
For
G
c
(
V
,
E
c
)
,
the
set
of
edges
is
E
c
=
{
e
c
(
v
x
,
v
y
)
|
v
x
∈
V
,
v
y
∈
V
,
v
x
=
}
(
,
)
v
y
. Using a linear combination, each edge
e
c
v
x
v
y
can be generated from
T
).
Therefore, the purpose is to learn optimal combination weights
w
to combine rela-
tions as well as optimal ranking method
h
j
on
G
c
:
(
,
)
=[
,...,
]
∑
i
∈{
1
,...,
m
}
w
i
e
i
v
x
v
y
,where
w
i
is the
i
-th element of
w
(i.e.
w
w
1
w
m
j
r
∗
)
.
<
w
,
>
=
argmax
Cor
(
r
c
,
j
,
(3)
w
,
h
j
∈{
h
1
,...,
h
s
}
Cai et al. [3] examine a similar idea with this approach: They attempt to identify the
best combination of relations (i.e. relations as features) which makes the relation
between the intra-community examples as tight as possible. Simultaneously, the
relation between the inter-community examples is as loose as possible when a user
provides multiple community examples (e.g. two groups of researchers). However,
our purpose is learn a ranking model (e.g. ranking of companies) based on social
networks, which has a different optimization task. Moreover, we propose innovative
features for entities based on combination or integration of structural importance
generated from social networks.
For this study, we simply use Boolean type (
w
i
) to combine relations.
Using relations of
m
types to combine a network, we can create 2
m
∈{
1
,
0
}
1 types of
combination-relational networks (in which at least one type of relation exists in the
G
c
). We obtain network rankings in these combined networks to learn and predict
the target rankings. Future work on how to choose parameter values will be helpful
to practitioners.
−
4.3
Network-Based Feature Integration Model
The proposed method in our research is to integrate multiple indices that are ob-
tained from multiple social networks to learn the target rankings. A feature by itself
(e.g. a centrality value) might have little correlation with the target ranking, but
when it is combined with some other features, they might be strongly correlated
with the target rankings [14]. Simply, we can integrate various centrality values for
each actor, thereby combining different meanings of importance to learn the rank-
ing. Furthermore, we can generate additional relational and structural features from
a network for each, such as how many nodes are reachable, how many connections
one's friends have, and the connection status of one's friends. We might understand
something about the behavior and power of the individual while we predict their
ranking if we could know the structural position of individuals. Herein, we desig-
nate these features generated from networks as
network-based features
. The inter-
esting question is
how to generate network-based features from networks for each
,
and
how to integrate these features to learn and predict rankings
. Below we will
describe the approach.
