8.4. Applications of signed networks
109
towards other groups. In the embedding of Figure 8.5(b) and Figure 8.5(c), they are
placed further away from the other groups, which seems appropriate. However, this
is not the case in the L rw embedding. Other nodes in the L rw embedding also show
reversed placement of the kind shown in the toy dataset. From both a mathematical
and practical point of view, our two proposed signed Laplacian embedding methods
are better than the signed Laplacian embedding methods in Kunegis et al. [48].
The embeddings of L sns and L bns are similar to one another. However, if we
look at the differences between the two signed Laplacian embeddings, members of
each subgroup are closer to one another in the L bns embedding than they are in L sns
embedding. The L bns embedding seems to work well rendering this network.
The measures for the Eastern Central Highlands of New Guinea dataset, with
distances computed in three dimensions since there are three groupings, are shown
in Table 8.1.
AER ANR MER
L rw 0.42
0.40
0.42
L sns 0.39
0.40
0.40
L bns 0.39
0.40
0.35
Table 8.1: Ratios for the Eastern Central Highlands of New Guinea embeddings
—smaller values are better
The ANR values for the three embeddings are similar. The L bns embedding
arguably produces the best embedding overall, especially for the MER score which
ignores extreme values.
Sampson monastery network
We use another small dataset derived from Sampson’s 1969 unpublished doctoral
thesis (the data available from the UCINET repository). The data comes from 18
trainee monks who were asked for opinions about their relationships over a period
of time in which the group they formed was disintegrating. The monks were asked
about who influenced them positively and negatively, whom they esteemed or despised, and whom they praised or blamed, but almost all of the analysis has focused
on the like/dislike ratings. Almost any technique applied to the matrix produces four
clusters that agree with those that Sampson originally postulated (for example, [29]).
The network is directed so we add the transpose to produce an undirected network,
ignoring the possibility that A likes B but B dislikes A. For simplicity, we also ignore
the difference of the like/dislike ratings.
The Sampson monastery dataset embeddings based on the three signed Laplacians are shown in Figure 8.6. In all three embeddings the positive (solid) edges are
short, and the negative (dashed) edges are long. The negative edges are not only
between groups, but also within groups. Figure 8.6 shows that the known group
structure is clearly visible in all three embeddings.
109
towards other groups. In the embedding of Figure 8.5(b) and Figure 8.5(c), they are
placed further away from the other groups, which seems appropriate. However, this
is not the case in the L rw embedding. Other nodes in the L rw embedding also show
reversed placement of the kind shown in the toy dataset. From both a mathematical
and practical point of view, our two proposed signed Laplacian embedding methods
are better than the signed Laplacian embedding methods in Kunegis et al. [48].
The embeddings of L sns and L bns are similar to one another. However, if we
look at the differences between the two signed Laplacian embeddings, members of
each subgroup are closer to one another in the L bns embedding than they are in L sns
embedding. The L bns embedding seems to work well rendering this network.
The measures for the Eastern Central Highlands of New Guinea dataset, with
distances computed in three dimensions since there are three groupings, are shown
in Table 8.1.
AER ANR MER
L rw 0.42
0.40
0.42
L sns 0.39
0.40
0.40
L bns 0.39
0.40
0.35
Table 8.1: Ratios for the Eastern Central Highlands of New Guinea embeddings
—smaller values are better
The ANR values for the three embeddings are similar. The L bns embedding
arguably produces the best embedding overall, especially for the MER score which
ignores extreme values.
Sampson monastery network
We use another small dataset derived from Sampson’s 1969 unpublished doctoral
thesis (the data available from the UCINET repository). The data comes from 18
trainee monks who were asked for opinions about their relationships over a period
of time in which the group they formed was disintegrating. The monks were asked
about who influenced them positively and negatively, whom they esteemed or despised, and whom they praised or blamed, but almost all of the analysis has focused
on the like/dislike ratings. Almost any technique applied to the matrix produces four
clusters that agree with those that Sampson originally postulated (for example, [29]).
The network is directed so we add the transpose to produce an undirected network,
ignoring the possibility that A likes B but B dislikes A. For simplicity, we also ignore
the difference of the like/dislike ratings.
The Sampson monastery dataset embeddings based on the three signed Laplacians are shown in Figure 8.6. In all three embeddings the positive (solid) edges are
short, and the negative (dashed) edges are long. The negative edges are not only
between groups, but also within groups. Figure 8.6 shows that the known group
structure is clearly visible in all three embeddings.