A Good View for Graph Contrastive Learning

. 2024 Feb 27;26(3):208. doi: 10.3390/e26030208

Algorithm 1 Coding tree with height k via structural entropy minimization.

Input: a graph

G = (V, E)

, a positive integer

k > 1

Output: a coding tree T with height k

1:
Generate a coding tree T with a root node $v_{r}$ and all nodes in $V$ as leaf nodes;
2:
// Stage 1: Bottom to top construction;
3:
while $| v_{r} . c h i l d r e n | > 2$ do
4:
Select $v_{i}$ and $v_{j}$ from $v_{r} . c h i l d r e n$ , conditioned on

$a r g m a x_{(v_{i}, v_{j})} {H^{T} (G) - H^{T_{MERGE (v_{i}, v_{j})}} (G)}$ ;
5:
$MERGE (v_{i}, v_{j})$ ;
6:
end while
7:
// Stage 2: Compress T to the certain height k;
8:
while $Height (T) > k$ do
9:
     Select $v_{i}$ from T, conditioned on

      $a r g m i n_{v_{i}} {H^{T_{REMOVE (v_{i})}} (G) - H^{T} (G) |$

                $v_{i} \neq v_{r} & v_{i} \notin V}$ ;
10:
$REMOVE (v_{i})$ ;
11:
end while
12:
// Stage 3: Fill T to avoid cross-layer links;
13:
for $v_{i} \in T$ do
14:
if $| Height (v_{i} . p a r e n t) - Height (v_{i}) | > 1$ then
15:
insert a new node $v_{ε}$ between $v_{i}$ and $v_{j}$ ;
16:
end if
17:
end for
18:
return T;