# Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning

arXiv: https://arxiv.org/abs/2007.16002 · HTML: https://mlsanity.com/paper/2007.16002/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 30 of 51)

- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Dissecting the Diffusion Process in Linear Graph Convolutional Networks](https://mlsanity.com/paper/2102.10739/) (2021)
- [Single Node Injection Attack against Graph Neural Networks](https://mlsanity.com/paper/2108.13049/) (2021)
- [Variational Graph Normalized Auto-Encoders](https://mlsanity.com/paper/2108.08046/) (2021)
- [PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering](https://mlsanity.com/paper/2312.14438/) (2023)
- [Signed Bipartite Graph Neural Networks](https://mlsanity.com/paper/2108.09638/) (2021)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Bundle Neural Networks for message diffusion on graphs](https://mlsanity.com/paper/2405.15540/) (2024)
- [Diffuser: Efficient Transformers with Multi-hop Attention Diffusion for Long Sequences](https://mlsanity.com/paper/2210.11794/) (2022)
- [Handling Missing Data via Max-Entropy Regularized Graph Autoencoder](https://mlsanity.com/paper/2211.16771/) (2022)
- [Adversarial Camouflage for Node Injection Attack on Graphs](https://mlsanity.com/paper/2208.01819/) (2022)
- [Adversarial Attack Framework on Graph Embedding Models with Limited Knowledge](https://mlsanity.com/paper/2105.12419/) (2021)
- [Company-as-Tribe: Company Financial Risk Assessment on Tribe-Style Graph with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2301.13492/) (2023)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [Multi-View Graph Representation Learning Beyond Homophily](https://mlsanity.com/paper/2304.07509/) (2023)
- [Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecasting](https://mlsanity.com/paper/2305.06587/) (2023)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Learning to Approximate Adaptive Kernel Convolution on Graphs](https://mlsanity.com/paper/2401.11840/) (2024)
- [Node Injection for Class-specific Network Poisoning](https://mlsanity.com/paper/2301.12277/) (2023)
- [L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification](https://mlsanity.com/paper/2403.06064/) (2024)
- [HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations](https://mlsanity.com/paper/2505.15405/) (2025)
- [QDC: Quantum Diffusion Convolution Kernels on Graphs](https://mlsanity.com/paper/2307.11234/) (2023)
- [Graph Representation Learning Beyond Node and Homophily](https://mlsanity.com/paper/2203.01564/) (2022)
- [Graph Adversarial Immunization for Certifiable Robustness](https://mlsanity.com/paper/2302.08051/) (2023)
- [Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification](https://mlsanity.com/paper/2305.16239/) (2023)
- [Self-supervised Learning and Graph Classification under Heterophily](https://mlsanity.com/paper/2306.08469/) (2023)

## Abstract (arXiv)

Graph convolutional networks gain remarkable success in semi-supervised learning on graph structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph structure. Previous methods, spectral methods and spatial methods, devote to defining graph convolution as a weighted average over neighboring nodes, and then learn graph convolution kernels to leverage the smoothness to improve the performance of graph-based semi-supervised learning. One open challenge is how to determine appropriate neighborhood that reflects relevant information of smoothness manifested in graph structure. In this paper, we propose GraphHeat, leveraging heat kernel to enhance low-frequency filters and enforce smoothness in the signal variation on the graph. GraphHeat leverages the local structure of target node under heat diffusion to determine its neighboring nodes flexibly, without the constraint of order suffered by previous methods. GraphHeat achieves state-of-the-art results in the task of graph-based semi-supervised classification across three benchmark datasets: Cora, Citeseer and Pubmed.