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from the respective scenario, the node degree should be taken into account while
assigning the relatedness scores to semantic edges.
For figuring out adequate scaling models, the analysis of the node degree distrib-
ution usually is a good starting point for defining a dataset specific scaling strategy.
Typical scaling models for social network data are based on power law probability
distributions. The scaling is done using logarithmic or polynomial scaling functions.
Adequate parameters should be learned based on training data. In the experiments
conducted in our evaluations we found that the applied scaling models have a strong
impact on the recommendation quality [
21
]. Inadequate scaling models or
missing
scaling models cannot be repaired in the later steps.
5.3.4.4 Path-Based Relatedness Models
Semantic datasets represent knowledge as a large graph consisting of nodes and
edges. In order to compute recommendations, a measure is needed for calculating the
relatedness between all node pairs taking into account the edges between the nodes.
In the previous sections, we explained how to assign relatedness scores to directly
connected nodes. In this section we focus on
edge algebras
allowing us to assign
relatedness scores also for node pairs connected by complex paths (characterized by
parallel edges and long edge sequences).
First, we define criteria according to which the score for complex path should be
computed [
21
]:
•
If two nodes are directly connected by exactly one edge, the relatedness of the
nodes is defined based on the edge weight.
•
Two nodes are the more semantically related the more parallel paths between the
nodes exist.
•
Two nodes are the less semantically related the longer the path between the nodes.
We analyze three different approaches for combining the edge weights. Our
approaches are based on the
distance
between nodes. We define the distance between
two nodes as the reciprocal of the relatedness score. Thus, great distance value result
Table 5.2
The table shows the formulas for calculating the path weights for (a) parallel edges and
(b) for a sequence of edges
Weighted path
Resistance distance
Shortest path
n
min
i
i
=
0
w
i
n
1
i
=
0
w
i
(a)
w
0
w
1
w
=
w
=
0
w
i
w
=
=
w
n
i
=
0
w
i
i
=
0
w
i
i
=
0
w
i
n
n
n
w
0
w
1
w
n
n
(b)
...
w
=
γ
w
=
w
=
The discount factor
γ
ensures that short paths get a higher weighting than long paths
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