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Graph Neural Networks (GNN) - Coggle Diagram
Graph Neural Networks (GNN)
are
Neural Networks
for
Graph Structured Data
without
assumption of Geometry
is a set of
Unordered Nodes
2 main desiderata
Permutation Invariance
Permutation Equivariance
processing for
Isomorphic Graphs
should yield
Same Result
for
Simplified Graph
Graph has only nodes
G = (X)
Features of node i
xi ∈ R^k
Node feature matrix of shape n x k:
X = (x1, x2, .......xn)^T
Requirement
design a function
f(X)
over the set
that does not depend on
Node Order
are changed by
Permutation operations (n!)
1 more item...
i.e. applying
P
2 more items...
General Blueprint:
Stacked Permutation Equivariant Functions
with potentially a tail of
Permutation Invariant Function
Augmented Simplified Graph
Desiderata
Invariance
Equivariance
Adjacency Matrix A:
Graph has nodes and edges
augment the set of nodes with edges between them.
Locality on Graphs
Concept of a node’s neighbourhood
For a node i, its (1-hop) neighbourhood:
