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Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms
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Introduces the local Euler Characteristic Transform (l-ECT), which encodes each node's k-hop neighborhood as a vector fed to XGBoost for node classification, plus a rotation-invariant ECT-based metric for aligning geometric data.
Problem
Message-passing GNNs aggregate neighbor features and can lose critical local information, especially under heterophily; a lossless, interpretable local representation of graph neighborhoods is needed.
Approach
Extends the global Euler Characteristic Transform to local k-hop neighborhoods (l-ECT), giving a sampled vector fingerprint per node that is theoretically sufficient to reconstruct 1-hop features and is used with a non-GNN classifier (XGBoost); also defines a rotation-invariant ECT metric for alignment.
Key results
- On WebKB, l-ECT1 reaches 81.2% on Wisconsin versus 70.2% for H2GCN and 49.7% for GIN.
- On Roman Empire, l-ECT1+l-ECT2 reaches 81.1% accuracy versus 77.4% for GraphSAGE and 76.4% for GAT.
- Across datasets, the worst l-ECT variant (l-ECT2) has a better average rank than every non-l-ECT baseline, with l-ECT1+l-ECT2 at average rank 2.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ℓ-ECT₁ + ℓ-ECT₂ instead of GraphSAGE | node classification · Cornell | accuracy: 76.0 ± 3.5 -> 67.1 ± 4.1 | Hurt |
| Use ℓ-ECT₁ instead of GraphSAGE | node classification · Wisconsin | accuracy: 72.9 ± 1.9 -> 81.2 ± 2.9 | Helped |
| Use ℓ-ECT₁ + ℓ-ECT₂ instead of H2GCN | node classification · Texas | accuracy: 72.3 ± 3.0 -> 74.8 ± 3.1 | Helped |
| Use ℓ-ECT₁ + ℓ-ECT₂ instead of GAT | node classification · Amazon Ratings | accuracy: 44.6 ± 0.9 -> 49.8 ± 0.3 | Helped |
| Use ℓ-ECT₁ + ℓ-ECT₂ instead of GraphSAGE | node classification · Roman Empire | accuracy: 77.4 ± 0.8 -> 81.1 ± 0.4 | Helped |
| Use ℓ-ECT₁ + ℓ-ECT₂ instead of GAT | node classification · Amazon Computers | accuracy: 92.4 ± 1.3 -> 92.2 ± 0.6 | Hurt |
| Use ℓ-ECT₁ + ℓ-ECT₂ instead of H2GCN | node classification · Chameleon | accuracy: 62.7 ± 1.6 -> 43.9 ± 0.7 | Hurt |
| Add ℓ-ECT₂ to ℓ-ECT₁ (ablation) | XGBoost node classifier · Actor | accuracy: 31.4 ± 1.9 -> 30.9 ± 0.7 | Hurt |
| Add ℓ-ECT₂ to ℓ-ECT₁ (ablation) | XGBoost node classifier · Cornell | accuracy: 66.8 ± 4.2 -> 67.1 ± 4.1 | No clear effect |
| Add ℓ-ECT₂ to ℓ-ECT₁ (ablation) | XGBoost node classifier · Amazon Ratings | accuracy: 48.4 ± 0.3 -> 49.8 ± 0.3 | Helped |
| Add ℓ-ECT₂ to ℓ-ECT₁ (ablation) | XGBoost node classifier · Roman Empire | accuracy: 80.4 ± 0.4 -> 81.1 ± 0.4 | Helped |
| Use 4096 rather than 0 randomly sampled ℓ-ECT₁ entries (ablation) | XGBoost node classifier · Coauthor CS | accuracy: 92.1 -> 92.6 | No clear effect |
Surprising findings
- Simple XGBoost on l-ECT features without hyperparameter tuning matches or beats tuned GNNs on many heterophilous benchmarks.
- On Amazon Computers and Actor, GIN and some l-ECT variants are not uniformly best; GAT wins Computers.
Limitations
- Naive l-ECT computation grows with k and graph size and density.
- Gains are weaker on some datasets (Chameleon, Squirrel, Computers), where H2GCN or GAT are best.
- Experiments use XGBoost without task-specific tuning, and baseline GNNs were trained with a fixed protocol, so comparisons are not state-of-the-art claims.
Experimental setup
Datasets: WebKB (Cornell, Wisconsin, Texas) Roman Empire Amazon Ratings Amazon Computers Amazon Photo Actor Chameleon Squirrel Cora CiteSeer PubMed WikiCS
Benchmarks: WebKB Roman Empire Amazon Ratings Amazon Computers Amazon Photo Actor Chameleon Squirrel Cora CiteSeer PubMed WikiCS
Metrics: accuracy critical difference rank Hausdorff distance squared L2 distance
Baselines: GCN GAT GIN GraphSAGE H2GCN
Builds on: Euler Characteristic Transform graph attention networks H2GCN XGBoost
Closest papers by meaning
- Differentiable Euler Characteristic Transforms for Shape Classification (ICLR 2024 · similarity 0.91)
- GraphGPT: Generative Pre-trained Graph Eulerian Transformer (ICML 2025 · similarity 0.87)
- Transitivity-Preserving Graph Representation Learning for Bridging Local Connectivity and Role-Based Similarity (AAAI 2024 · similarity 0.86)
- Subgraph Invariant Learning Towards Large-Scale Graph Node Classification (AAAI 2025 · similarity 0.85)
- Learning Efficient Positional Encodings with Graph Neural Networks (ICLR 2025 · similarity 0.85)
- Towards Principled Graph Transformers (NeurIPS 2024 · similarity 0.85)
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