Hypergraph Neural Additive Networks

In this project, we designed an interpretable hypergraph learning model for both node and hyperedge prediction tasks called HyperGraph Neural Additive Networks (HGNAN). HGNAN extends the idea of Neural Additive Models (NAMs) to hypergraph learning by integrating it with hypergraph distance-based structural information. The following figure gives an overview of our proposed model’s architecture：

Figure: Pipeline of the project.

Highlights

  • ✅ HGNAN can achieve on-par performance on node classification tasks while outperforming SOTA models by >10% on real-world hyperedge prediction tasks (e.g.recovering missing reactions in metabolic networks).
  • ✅ HGNAN provides extra strength of providing a clear visualization of its decision making process and enabling domain experts to easily debug the model and intervene.

Method Sketch

HGNAN learns two components: a set of distance modules ${\rho_s(\cdot)}{s=1}^{s{\text{max}}}$ and a set of feature shape functions ${f_k(\cdot)}_{k=1}^{K}$. The distance module $\rho_s(\cdot)$ learns a distance function on the $s$-intersection graph, whereas each $f_k(\cdot)$ models a univariate shape for feature $k$.

The embedding for each node $i$ on the $s$-intersection graph is denoted $h_i^{(s)}$, computed by combining the $s$-level distance function with the feature shape functions. For node prediction tasks we use neighborhood-level aggregation; for hyperedge prediction tasks we use graph-level aggregation.

After obtaining $h_i^{(s)}$, the final embedding for node $i$ is a weighted sum of ${h_i^{(s)}}{s=1}^{s{\text{max}}}$ used for downstream tasks.

Results

Performance:

Comparison of test accuracy (mean ± standard deviation) between HGNAN-node and baselines across node classification datasets. Bold indicates the highest test accuracy.
Method Zoo Mushroom NTU2012 Pokec Actor Avg. Rank
MLP 0.887 ± 0.052 0.965 ± 0.006 0.853 ± 0.012 0.580 ± 0.019 0.827 ± 0.004 6
AllDeepSets 0.942 ± 0.042 0.999 ± 0.001 0.876 ± 0.014 0.567 ± 0.008 0.838 ± 0.003 4.8
AllSetTransformer 0.973 ± 0.032 0.999 ± 0.001 0.890 ± 0.011 0.572 ± 0.010 0.836 ± 0.002 3.4
ED-HNN 0.950 ± 0.035 0.998 ± 0.002 0.895 ± 0.013 0.618 ± 0.020 0.856 ± 0.006 3.2
HGNN 0.957 ± 0.022 0.998 ± 0.001 0.872 ± 0.014 0.553 ± 0.014 0.744 ± 0.004 5.6
HyperGCN 0.423 ± 0.000 0.482 ± 0.000 0.796 ± 0.033 0.538 ± 0.014 0.630 ± 0.000 8
UniGCNII 0.950 ± 0.048 0.999 ± 0.001 0.893 ± 0.016 0.570 ± 0.018 0.828 ± 0.003 4.2
HGNAN-node (ours) 0.953 ± 0.030 0.999 ± 0.001 0.890 ± 0.011 0.634 ± 0.012 0.857 ± 0.004 3
Comparison of hyperedge prediction accuracy (mean ± standard deviation) across four BiGG GEM datasets: iAF1260b, iJR904, iSB619, and iYO844. Bold marks the best per dataset. HGNAN-edge outperforms all baselines.
Method iAF1260b iJR904 iSB619 iYO844
CHESHIRE 0.834 ± 0.050 0.732 ± 0.068 0.730 ± 0.038 0.893 ± 0.047
NHP 0.732 ± 0.076 0.690 ± 0.090 0.687 ± 0.055 0.747 ± 0.043
HyperSAGNN 0.730 ± 0.075 0.753 ± 0.056 0.729 ± 0.162 0.708 ± 0.045
HGNAN-edge (ours) 0.935 ± 0.069 0.958 ± 0.026 0.977 ± 0.008 0.952 ± 0.181

Interpretability

Here we provide a small demo for visualization of HGNAN on Zoo dataset.

Visualization on Zoo dataset. LHS is visualization for binary feature shape function; RHS is feature importance.

References