Information Technology Reference
In-Depth Information
Ta b l e 1
Operator list
Notation Input
Output
Description
C
(
1
)
x
node
x
a nodeset
adjacent nodes to
x
C
(
k
)
node
x
a nodeset
nodes within distance
k
from
x
x
s
(
1
)
a nodeset
a list of values 1 if connected, 0 otherwise
t
a nodeset
a list of values distance between a pair of nodes
t
x
a nodeset
a list of values distance between node
x
and other nodes
γ
a nodeset
a list of values number of links in each node
u
x
a nodeset
a list of values 1 if the shortest path includes node
x
, 0 other-
wise
Avg
a list of values a value
average of values
Sum
a list of values a value
summation of values
Min
a list of values a value
minimum of values
Max
a list of values a value
maximum of values
ratio of value on neighbor nodeset
C
(
1
)
Ratio
two values
value
by
x
reachable nodeset
C
(
∞
)
x
centrality measures and other SNAs indices for each node. Below, we describe other
examples used in the social network analysis literature.
•
network diameter:
Min
◦
t
◦
N
•
characteristic path length:
Avg
◦
t
◦
N
s
(
1
)
C
(
1
)
•
degree centrality:
Sum
◦
◦
x
x
C
(
1
)
s
(
1
)
◦
•
node clustering:
Avg
◦
x
C
(
∞
)
•
closeness centrality:
Avg
◦
t
x
◦
x
C
(
∞
)
•
betweenness centrality:
Sum
◦
u
x
◦
,
x
C
(
1
)
•
structural holes:
Avg
◦
t
◦
x
N
(
1
x
in a feature vector equal to 1, and all others
to 0, we can elucidate the effect of degree centrality for predicting target ranking.
s
(
1
)
When we set the element
Sum
◦
◦
x
4.3.3
Network-Based Feature Integration
After we generate various network-based features for individual nodes, we integrate
them to learn the ranking. We introduce an
f
-dimensional feature vector
F
,inwhich
each element represents a network-based feature for each node. We identify the
f
-dimensional combination vector
u
T
to combine network-based fea-
tures for each node. The inter-product
u
T
F
for each node produces an
n
-dimensional
ranking. For relational networks of
m
kinds, the feature vector can be expanded to
m
=[
u
1
,...,
u
f
]
60 dimensions. In this case, the purpose is finding out whether optimal combi-
nation weight
u
maximally explains the target ranking:
×
u
T
r
∗
)
,
u
=
argmax
u
Cor
(
•
F
,
(4)
