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Unsupervised Neighborhood Propagation Kernel Layers for Semi-supervised Node Classification

AAAI 2024 · Graph learning › Graph self-supervised learning · approach: Semi-supervised node representation learning · 6 citations (OpenAlex)

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Proposes Graph Convolutional Kernel Machine (GCKM), a deep kernel machine with unsupervised kernel-PCA one-hop propagation layers and a semi-supervised kernel spectral clustering read-out, trained in dual variables for few-label node classification.

Problem

Semi-supervised node classification when very few labels are available; existing GNNs use parametric regression-based cores and kernel methods for graphs have not been effectively applied to node-level tasks with message passing.

Approach

Stack unsupervised kernel PCA layers doing one-hop neighborhood aggregation (learning dual node representations directly, with implicit feature maps) and a semi-supervised kernel spectral clustering read-out derived via Fenchel-Young inequality and restricted kernel machine duality; train with Stiefel-constrained Cayley Adam plus linear-system updates.

Key results

• With few labels, GCKM reaches 80.74% on Cora and 58.03% on OGB-Arxiv, outperforming GNN baselines in 5 of 6 datasets; GCKM-MV reaches 38.15% on Chameleon and 29.11% on Squirrel.
• In the 1-layer to 10-layer ablation on Cora, GCKM stays around 80% at 2 to 10 layers while GCN drops to 72.69% at 10 layers.
• In node clustering, GCKM obtains NMI 49.0 on Cora and 37.5 on CiteSeer, versus 48.8 and 33.7 for DMoN.

Measured effects reported in the paper

Surprising findings

• The linear system in the semi-supervised layer is about 98% sparse in experiments, which the authors attribute to small r_i values.
• With no validation labels, selecting by the unsupervised cosine-distance metric still gives a usable model, whereas GNN baselines cannot perform early stopping.

Limitations

• Scaling to very large graphs requires a proper sparse solver, which is not yet implemented.
• Only one-hop propagation per layer; the method is limited to transductive node classification in the current version.
• Hyperparameter search is random for GCKM and grid for baselines; DMoN's NMI on PubMed (29.8) exceeds GCKM's (25.2).

Experimental setup

Datasets: Cora CiteSeer PubMed OGB-Arxiv Chameleon Squirrel

Benchmarks: Cora CiteSeer PubMed OGB-Arxiv Chameleon Squirrel

Metrics: test accuracy NMI

Baselines: SVM-rbf SVM-diff SVM-wwl MLP GCN APPNP GPR-GNN BernNet ChebNetII DMoN

Builds on: restricted kernel machine kernel spectral clustering GCN GIN Cayley Adam

Closest papers by meaning

• Rethinking Kernel Methods for Node Representation Learning on Graphs (NeurIPS 2019 · similarity 0.90)
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