Definition
Position-aware GNN (P-GNN) is designed to compute position-aware Node Embedding.
Architecture
Effective Node Embedding should be able to learn to distinguish nodes and . However, standard GNN is not able to classify nodes and into different classes based on the network structure alone because the two nodes are symmetric/isomorphic in the graph, and their GNN rooted subtrees used for message aggregation are the same.
Anchor-Set
By using the distance of a given target node to each anchor-set as an augmented node feature, P-GNN can deal with the position-aware tasks. Where anchor-sets are randomly constructed.
P-GNN first samples sets of anchor nodes, computes the distance of a given target node to each anchor-set, and then learns a permutation-invariant aggregation over the anchor-sets. The model can capture positions/locations of nodes with respect to the anchor nodes.