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HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph Representation Learning
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Proposes HC-GAE, a hierarchical cluster-based graph auto-encoder that uses hard assignment to split graphs into isolated subgraphs in the encoder and soft assignment to expand nodes in the decoder, evaluated on node and graph classification benchmarks.
Problem
GAEs struggle to produce universal representations for both node-level and graph-level downstream tasks (topological missing from over-emphasis on node features) and suffer from over-smoothing in deep GNN encoders/decoders.
Approach
Encoder decomposes the graph via hard node assignment into separated subgraphs, compressing each into a coarsened node so message passing stays within subgraphs; decoder uses soft assignment to expand coarsened nodes back to the original graph; the loss sums a local subgraph KL term (regularizer) and a global reconstruction term over features and structure.
Key results
- Node classification: HC-GAE reaches 87.97% on Cora and 75.29% on CiteSeer, average rank 1.2 across 5 datasets (vs. S2GAE 86.15% and 74.60%).
- Graph classification: HC-GAE reaches 92.38% on MUTAG and 78.13% on PROTEINS, average rank 1.2; S2GAE slightly beats it on COLLAB (81.02 vs 80.41).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HC-GAE instead of S2GAE | Node classification · Cora | accuracy: 86.15$\pm$0.25 -> 87.97$\pm$0.10 | Helped |
| Use HC-GAE instead of S2GAE | Node classification · CiteSeer | accuracy: 74.60$\pm$0.06 -> 75.29$\pm$0.09 | Helped |
| Use HC-GAE instead of S2GAE | Node classification · PubMed | accuracy: 86.91$\pm$0.28 -> 87.56$\pm$0.35 | Helped |
| Use HC-GAE instead of S2GAE | Node classification · Computers | accuracy: 90.94$\pm$0.08 -> 91.07$\pm$0.14 | Helped |
| Use HC-GAE instead of GraphMAE | Node classification · CS | accuracy: 93.47$\pm$0.04 -> 92.28$\pm$0.07 | Hurt |
| Use HC-GAE instead of S2GAE | Graph classification · IMDB-B | accuracy: 75.76$\pm$0.62 -> 76.72$\pm$0.60 | Helped |
| Use HC-GAE instead of S2GAE | Graph classification · IMDB-M | accuracy: 51.79$\pm$0.36 -> 51.90$\pm$1.47 | Helped |
| Use HC-GAE instead of S2GAE | Graph classification · PROTEINS | accuracy: 76.37$\pm$0.43 -> 78.13$\pm$1.37 | Helped |
| Use HC-GAE instead of S2GAE | Graph classification · COLLAB | accuracy: 81.02$\pm$0.53 -> 80.41$\pm$0.02 | Hurt |
| Use HC-GAE instead of InfoGCL | Graph classification · MUTAG | accuracy: 91.20$\pm$1.30 -> 92.38$\pm$1.17 | Helped |
| Replace the separated-subgraph, hard-assignment encoder with soft assignment (HC-GAE-SE) (ablation) | HC-GAE · Graph classification | accuracy | Hurt |
Surprising findings
- GraphMAE scores higher than HC-GAE on the CS node classification dataset (93.47 vs 92.28).
Limitations
- Over-smoothing claim is argued qualitatively without direct empirical measurement.
- Baseline results are copied from prior papers where available, and some entries are N/A, so comparisons are not fully controlled.
- GraphMAE outperforms HC-GAE on the CS node classification dataset and S2GAE on COLLAB.
Experimental setup
Datasets: Cora CiteSeer PubMed Computers CS IMDB-B IMDB-M PROTEINS COLLAB MUTAG
Benchmarks: Cora CiteSeer PubMed Computers CS IMDB-B IMDB-M PROTEINS COLLAB MUTAG
Metrics: accuracy average rank
Baselines: DGI VGAE SSL-GCN GraphSage GraphMAE S2GAE WLSK DGCNN DiffPool Graph2Vec InfoGCL
Builds on: Graph Auto-Encoder GCN VGAE DiffPool
Closest papers by meaning
- GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction (NeurIPS 2024 · similarity 0.91)
- Dual Low-Rank Graph Autoencoder for Semantic and Topological Networks (AAAI 2023 · similarity 0.90)
- Effective Decoding in Graph Auto-Encoder Using Triadic Closure (AAAI 2020 · similarity 0.89)
- The quest for the GRAph Level autoEncoder (GRALE) (NeurIPS 2025 · similarity 0.89)
- Graph Positional and Structural Encoder (ICML 2024 · similarity 0.86)
- Teacher-guided Edge Discriminator for Personalized Graph Masked Autoencoder (AAAI 2025 · similarity 0.86)
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