Inferring Users’ Social Roles with a Multi-Level Graph Neural Network Model

. 2021 Nov 1;23(11):1453. doi: 10.3390/e23111453

Algorithm 1 Our embedding generation algorithm for directed graphs.

Input:

Digraph $G (V, E);$ hop K; input features $\{x_{v}, \forall v s . \in V\};$ weight matrices $W^{k}, \forall k \in {1, \dots, K}$ ; non-linearity $σ$ ; the aggregator functions: MeanLayer and AttentionLayer; the gate function: gate; the concatenate function: Concat; the neighborhood sampling function $N : v s . \to 2^{ν}$ ; the weight coefficient: $μ$

Output:
Node representations

z_{v}

for all

v \in V

1

h_{v}^{0} \leftarrow x_{v}, \forall v s . \in V

2

FOR

k = 1 \dots K

3

FOR

v \in V

4

IF

k = = 1

5

A g g r e g a t o r = M e a n L a y e r;

8

ELSE DO

5

A g g r e g a t o r = A t t e n t i o n L a y e r;

9

h_{N (v)}^{k} + \leftarrow A g g r e g a t o r (\{h_{u}^{k - 1}, \forall u \in N (v) +\});

10

h_{N (v)}^{k} - \leftarrow A g g r e g a t o r (\{h_{u}^{k - 1}, \forall u \in N (v) -\});

11

h_{N (v)}^{k} \leftarrow C o n c a t (h_{v}^{k - 1} +, h_{v}^{k - 1} -);

12

h_{v}^{k} \leftarrow σ (W^{k} \cdot h_{N (v)}^{k})

13

END

14

h_{v}^{k} \leftarrow h_{v}^{k} / {∥h_{v}^{k}∥}_{2}, \forall v s . \in V

15

END

16

z_{v} \leftarrow g a t e {h_{v}^{1}, \dots, h_{v}^{K}}, \forall v s . \in V