Hypergraph Learning with Line Expansion

A very interesting paper finished on Feb. 2020 when I was in my previous group. Unfortunately, I have been so reluctant and cannot find a chance to invest time for further improvements. Recently, I polished it a bit and get it into CIKM'22 Long Research Paper Track (lucky!). This work proposes an elegant hypergraph transformation (i.e., line expansion), which bijectively maps a hypergraph to a simple graph and enables all existing graph learning algorithms to work effortlessly on hypergraphs.

Hypergraphs are generalized graphs, which consist of vertices and hyperedges. One vertex in hypergraph can connect to multiple hyperedges and one hyperedge can connect to multiple vertices. Simple graphs are special 2-regular hypergraphs (since each edge only connect to two nodes).

1. Code Structure

• data/: under this folder, we provide several hypergraph datasets
  • 20newsW100, ModelNet40, Mushroom, NTU2012, zoo
• src/
  • layers.py: standard neural network layers
  • models.py: GCN, GAT, SpGAT (sparse GAT model)
  • utils.py: auxiliary functions
  • main.py: the running script
  • LE.py: the LE transformation script (from hypergraphs to graphs)
• config/: containing the hyperparameter configurations

2. Quick Start

2.1 Work with Our Hypergraphs

# select a dataset from 20newsW100, ModelNet40, Mushroom, NTU2012, zoo
python main.py --dataset [DATASET] --hidden 64 --dropout 0.5 --lr 0.02 --epochs 50

2.2 Work with Your Own Hypergraphs

• step 1: create a dataset folder under data/DATASET-NAME
• step 2: process your own hypergraphs into two files:
  • DATASET-NAME.content: each row is a data sample, starting by sample index, sample features (column based) and sample labels. For example, the first row of zoo.content:
    • 0 1 0 0 1 0 0 1 1 1 1 0 0 4 0 0 1 1
    • the first "0" means the sample index
    • the last "1" means label class is 1
    • other float-valued or categorical number in the middle are the features
  • DATASET-NAME.edges: each row is a (vertex index, hyperedge index) pair, the indices do not necessarily start from "0". In our code, we will reindex the vertices and hyperedges. For example, the first row of zoo.edges:
    • 2 101
    • "2" means the index for the vertex
    • "101" means the index for the hyperedge

3. Plug LE into Your Model?

step 1: transform the hypergraph into graph

• from src.LE import transform
• Just read the input and output instruction. Prepare your DATASET-NAME.edges and feed in.

  def transform(edges, v_threshold=30, e_threshold=30):
      """construct line expansion from original hypergraph
      INPUT:
          - edges <matrix>
              - size: N x 2. N means the total vertex-hyperedge pair of the hypergraph
              - each row contains the idx_of_vertex, idx_of_hyperedge
          - v_threshold: vertex-similar neighbor sample threshold
          - e_threshold: hyperedge-similar neighbor sample threshold
      Concept:
          - vertex, hyperedge: for the hypergraph
          - node, edge: for the induced simple graph
      OUTPUT:
          - adj <sparse coo_matrix>: N_node x N_node
          - Pv <sparse coo_matrix>: N_node x N_vertex
          - PvT <sparse coo_matrix>: N_vertex x N_node
          - Pe <sparse coo_matrix>: N_node x N_hyperedge
          - PeT <sparse coo_matrix>: N_hyperedge x N_node
      """
  

step 2: run your graph algorithm

# prepare your ```DATASET-NAME.content``` and get features as well as the labels
features, labels = content[:, 1:-1], content[:, -1]

# project features into LE domain
features = Pv @ features

# get embedding in LE graph domain
embedding = run_graph_algorithm(adj, features)

# project back to hypergraph domain
embedding_back = PvT @ embedding

# use FC layer to predict label
class_logit = fully_connected_layer(embedding_back)

4. Citation

If you think this is repo useful, please cite our paper. For question answering, please contact [email protected].

@article{yang2022hypergraph,
  title={Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansion},
  author={Yang, Chaoqi and Wang, Ruijie and Yao, Shuochao and Abdelzaher, Tarek},
  booktitle = {Proceedings of the 31st ACM International Conference on Information and Knowledge Management, {CIKM} 2022},
  year={2022}
}

@article{yang2020hypergraph,
  title={Hypergraph Learning with Line Expansion},
  author={Yang, Chaoqi and Wang, Ruijie and Yao, Shuochao and Abdelzaher, Tarek},
  journal={arXiv preprint arXiv:2005.04843},
  year={2020}
}