Papers › Rethinking Kernel Methods for Node Representation Learning on Graphs

Rethinking Kernel Methods for Node Representation Learning on Graphs

6 Oct 2019NeurIPS 2019 12arXiv:1910.02548archive 2025-07-28

Yu Tian, Long Zhao, Xi Peng, Dimitris N. Metaxas

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturing the structural information in a graph. We theoretically show that our formulation is as powerful as any positive semidefinite kernels. To efficiently learn the kernel, we propose a novel mechanism for node feature aggregation and a data-driven similarity metric employed during the training phase. More importantly, our framework is flexible and complementary to other graph-based deep learning models, e.g., Graph Convolutional Networks (GCNs). We empirically evaluate our approach on a number of standard node classification benchmarks, and demonstrate that our model sets the new state of the art.

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Code

bluer555/KernelGCN officialmentioned in papermentioned on GitHubpytorch report

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Tasks

Classification General Classification Graph Classification Graph Representation Learning Graph Similarity Link Prediction Node Classification Representation Learning

Results from the paper archive 2025-07-28

Task	Dataset	Model	Metric	Value	Rank at snapshot	Leaderboard	Report
Link Prediction	Citeseer	Node Feature Agg + Similarity Metric	AP	91.8%	#11 of 13	Archive leaderboard	report
Link Prediction	Citeseer	Node Feature Agg + Similarity Metric	AUC	90.9%	#11 of 13	Archive leaderboard	report
Link Prediction	Cora	BANE	AP	93.2%	#9 of 13	Archive leaderboard	report
Link Prediction	Cora	BANE	AUC	93.50%	#9 of 13	Archive leaderboard	report
Link Prediction	Pubmed	Node Feature Agg + Similarity Metric	AP	94.2%	#10 of 13	Archive leaderboard	report
Link Prediction	Pubmed	Node Feature Agg + Similarity Metric	AUC	94.5%	#10 of 13	Archive leaderboard	report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

Graph Convolutional Networks

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