DHT
DHT, which transforms the edges of a graph into the nodes of a hypergraph.
ENGNN, use hypergraph after DHT to propagation
Background
Before methods only capture edge information implicitly, e.g. used as weight.
Contribute
- propose DHT, Dual Hypergraph Transformation
- propose a novel edge representation learning scheme ENGNN by using DHT.
- propose novel edge pooling methods.
Method
DHT： how to transfer graph to hypergraph
Step1: Get origin graph representation
Firstly, we get the initial node feature and edge feature. \[ node \space feature: X\in R^{n\times d} \]
\[ edge\space feature: E\in R^{m\times d'} \]
Than we use an incidence matrix M rather than an adjacency matrix to represent graph structure. \[ incidence\space matrix: M\in \{0,1\}^{n\times m} \] So the origin graph is \[ G=(X,M,E) \]
Step 2: Use DHT to get hypergraph \(G^*\)
The hypergraph represent \[ G^*=(X^*,M^*,E^*) \]
\[ X^*=E \]
\[ M^*=M^T \]
\[ E^*=X \]
\[ DHT:G=(X,M,E)->G^*=(E,M^T,X) \]
While DHT is a bijective transformation: \[ DHT:G^*=(E,M^T,X)->G=(X,M,E) \]
EHGNN: an edge representation learning framework using DHT
\[ E^{(l+1)}=ENGNN(X^{(l)},M,E^{(l)})=GNN(DHT(X^{(l)},M,E^{(l)})) \]
So ENGNN consists of DHT and GNN, while GNN can be any GNN function.
After ENGNN, EHGNN, \(E^{(L)}\) is returned to the original graph by applying DHT to dual hypergraph \(G^∗\). Then, the remaining step is how to make use of these edge-wise representations to finish the task.
Pooling
To be continue...
Advantage
DHT
- low time complexity
