Edge Representation Learning with Hypergraphs
- 1. Edge Representation Learning with Hypergraphs Jaehyeong Jo1*, Jinheon Baek1*, Seul Lee1*, Dongki Kim1, Minki Kang1, Sung Ju Hwang1,2 (*: equal contribution) KAIST1, AITRICS2, South Korea
- 2. 1 3 2 4 A B C D 𝑮𝑮 = ( 𝑿𝑿, 𝑴𝑴, 𝑬𝑬 ) Edge Feature Node Feature Incidence Matrix 1 2 3 4 A B C D A B C D 1 2 3 4 Graphs: Nodes, Edges and Incidence Graphs can be represented by the triplet: Node feature, incidence matrix, and edge feature. 𝑿𝑿 𝑴𝑴 𝑬𝑬
- 3. Importance of Learning Edges (a) Tylenol (Beneficial) (b) NAPQI (Toxic) (c) Twitter network Previous works focus on accurately representing the nodes, largely overlooking edges which are essential components of a graph. http://allthingsgraphed.com/2014/11/02/twitter-friends-network/
- 4. Learning Edge Representation via Nodes Node-to-Node message passing A B C D 1 2 3 4 Edge-to-Node message passing Previous works have used edge features as auxiliary information to augment node features, which implicitly capture the edge information in the node representations.
- 5. Edge HyperGraph Neural Network (EHGNN) HyperCluster HyperDrop Input Graph 1 3 2 4 A B C D B A C D 1 2 3 4 Output Graph Global Edge Representation Message Passing Node-to-Hyperedge Edge-to-Node DHT Dual Hypergraph Transformation (DHT) Message Passing We propose a novel edge representation learning scheme using Dual Hypergraph Transformation, and two edge pooling methods, namely HyperCluster and HyperDrop.
- 6. Dual Hypergraph Transformation Dual Hypergraph Transformation Input Graph 𝑮𝑮 = (𝑿𝑿, 𝑴𝑴, 𝑬𝑬) Dual Hypergraph 𝑮𝑮∗ = (𝑿𝑿∗ , 𝑴𝑴∗ , 𝑬𝑬∗ ) (a) (b) (d) (c) (a) Edge-to-Node (d) Node-to-Edge (b) Node-to-Hyperedge (c) Hyperedge-to-Node 3 4 2 1 D 5 1 3 2 4 A B C D 5 5 1 3 2 4 A B D C B A C 1 2 3 4 5 𝑬𝑬 A 𝑴𝑴 B C D 1 2 3 4 5 𝑿𝑿 A B C D 𝑬𝑬∗ = 𝑿𝑿 A B C D A 𝑴𝑴∗ = 𝑴𝑴𝑻𝑻 B C D 1 2 3 4 5 1 2 3 4 5 𝑿𝑿∗ = 𝑬𝑬 We represent edges as nodes in a hypergraph, which allows us to apply any off-the- shelf message-passing schemes designed for node-level representation learning.
- 7. Message-Passing on the Dual Hypergraph Message-passing cost on the dual hypergraph is equal to the message-passing cost on the original graph as 𝑶𝑶(𝑬𝑬). DHT DHT Message-Passing Dual Hypergraph We can perform message-passing between edges of a graph, by performing message-passing between nodes of its dual hypergraph.
- 8. Edge Pooling: HyperCluster & HyperDrop HyperCluster HyperDrop Output Graph Global Edge Representations We propose two novel graph pooling methods to obtain compact graph-level edge representations, namely Hypercluster and HyperDrop. Representing each edge well alone is insufficient in obtaining an accurate representation of the entire graph.
- 9. Experiments • Graph Reconstruction • Graph Generation • Graph Classification • Node Classification : Generate a valid graph with desired properties. : Reconstruct node and edge features of a given graph from their pooled representations. : Predict the label of a given graph. : Predict the labels of the node of a given graph.
- 10. Graph Reconstruction Figure: Graph reconstruction results on the ZINC molecule (left) and synthetic (right) datasets. (a) Original (v) R-GCN + GMPool (b) MPNN + GMPool (d) HyperCluster (Ours) Accurately representing edges is crucial for graph reconstruction tasks. EHGNN with HyperCluster yields incomparably high performance compared to the baselines.
- 11. Graph Reconstruction: Compression Figure: Relative size of the representation after pooling to the original graph. We validated the effectiveness of HyperCluster in dense graph compression, in which our method is able to obtain highly compact but accurate representation.
- 12. Graph Generation Figure: Graph generation results on MolGAN (left) and MARS (right). EHGNN frameworks obtains significantly improved generation performance, with both MolGAN and MARS architectures.
- 13. Graph Classification Figure: Graph classification results on test sets. EHGNN with HyperDrop outperforms all the hierarchical pooling baselines, and when paired with GMT, obtains the best performance on most of the datasets.
- 14. Graph Classification: Examples Figure: HyperDrop results on COLLAB dataset. HyperDrop accurately identifies the task relevant edges, which leads to dividing the large graph into connected components for effective message passing.
- 15. Node Classification Figure: Node classification results on Cora (left) and Citeseer (right) datasets. HyperDrop alleviates the over-smoothing problem of deep GNNs on semi- supervised node classification tasks by identifying task relevant edges.
- 16. Conclusion • We introduce a novel edge representation learning scheme using Dual Hypergraph Transformation, which we can apply off-the-shelf message passing schemes designed for node-level representation learning. • We propose a novel edge pooling methods for graph-level representation learning, to overcome the limitations of existing node-based pooling methods. • We validate our methods on graph reconstruction, generation, and classification tasks, on which we largely outperform existing graph representation learning methods.