We study our proposed method on the multiple-network data of seventh-grade students' opinion data set (Vickers & Chan, 1981). Three directed networks were constructed in response to questions shown in Table 3. Setting the number of compressed nodes to be $k=2$ and applying the Tensor-StNMF in algorithm 3, we obtained two communities with node assignment weights shown in Figure 5, where the directed connections between two communities are from the vertices compressed in red to vertices compressed in blue. Interestingly, our detected communities largely characterize gender, since the first 13 students are boys and the rest are girls. These results show a directed trend where boys are more likely to prefer girls for working and playing. The auxiliary weights $rk$ in Table 3 show that this is strongest in choosing who to with, followed by choosing a working partner. In Figure 5, we visualize the character relationship network, with blue and red being the identified compressed nodes and yellow denoting students who do not belong to any of the compressed nodes. We use blue squares for girls in the compressed nodes with more boys and red squares for boys in the compressed nodes with more girls. We see that the blue and red vertices are highly connected and that the edges that go into the red compressed node are predominantly from the blue compressed node, while the edges going into the blue compressed node are from all vertices. The yellow labeled vertices, which belong to neither compressed node, are more sparsely connected in the network.
Figure 5:

Figure 5:

Table 3:

Seventh-Grade Students: Relational Networks and Corresponding Weights.

QuestionsRelations$rk$
Who do you get along with? Character 0.746
Who are your best friends? Emotional 0.398
Who you prefer to work with? Working 0.532
QuestionsRelations$rk$
Who do you get along with? Character 0.746
Who are your best friends? Emotional 0.398
Who you prefer to work with? Working 0.532
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