# Convolutional Kernel Networks for Graph-Structured Data

arXiv: https://arxiv.org/abs/2003.05189 · HTML: https://mlsanity.com/paper/2003.05189/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2020.

## Built on by (most cited first, 30 of 38)

- [GraphiT: Encoding Graph Structure in Transformers](https://mlsanity.com/paper/2106.05667/) (2021)
- [Transformer for Graphs: An Overview from Architecture Perspective](https://mlsanity.com/paper/2202.08455/) (2022)
- [KerGNNs: Interpretable Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/2201.00491/) (2022)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Prototypical Graph Contrastive Learning](https://mlsanity.com/paper/2106.09645/) (2021)
- [Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels](https://mlsanity.com/paper/2104.02995/) (2021)
- [KGNN: Harnessing Kernel-based Networks for Semi-supervised Graph Classification](https://mlsanity.com/paper/2205.10550/) (2022)
- [Learning Long Range Dependencies on Graphs via Random Walks](https://mlsanity.com/paper/2406.03386/) (2024)
- [How Expressive are Transformers in Spectral Domain for Graphs?](https://mlsanity.com/paper/2201.09332/) (2022)
- [Graph Kernel Neural Networks](https://mlsanity.com/paper/2112.07436/) (2021)
- [Flatten Graphs as Sequences: Transformers are Scalable Graph Generators](https://mlsanity.com/paper/2502.02216/) (2025)
- [Capturing Graphs with Hypo-Elliptic Diffusions](https://mlsanity.com/paper/2205.14092/) (2022)
- [Weisfeiler and Leman Go Walking: Random Walk Kernels Revisited](https://mlsanity.com/paper/2205.10914/) (2022)
- [State of the Art and Potentialities of Graph-level Learning](https://mlsanity.com/paper/2301.05860/) (2023)
- [Spatial Graph Attention and Curiosity-driven Policy for Antiviral Drug Discovery](https://mlsanity.com/paper/2106.02190/) (2021)
- [Descriptive Kernel Convolution Network with Improved Random Walk Kernel](https://mlsanity.com/paper/2402.06087/) (2024)
- [From Quantum Graph Computing to Quantum Graph Learning: A Survey](https://mlsanity.com/paper/2202.09506/) (2022)
- [Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation](https://mlsanity.com/paper/2311.09500/) (2023)
- [Permute Me Softly: Learning Soft Permutations for Graph Representations](https://mlsanity.com/paper/2110.01872/) (2021)
- [Graph-wise Common Latent Factor Extraction for Unsupervised Graph Representation Learning](https://mlsanity.com/paper/2112.08830/) (2021)
- [Unsupervised Neighborhood Propagation Kernel Layers for Semi-supervised Node Classification](https://mlsanity.com/paper/2301.13764/) (2023)
- [MoSE: Unveiling Structural Patterns in Graphs via Mixture of Subgraph Experts](https://mlsanity.com/paper/2509.09337/) (2025)
- [Generalized Reference Kernel for One-class Classification](https://mlsanity.com/paper/2205.00534/) (2022)
- [The PWLR Graph Representation: A Persistent Weisfeiler-Lehman scheme with Random Walks for Graph Classification](https://mlsanity.com/paper/2208.13427/) (2022)
- [Graph Transformers without Positional Encodings](https://mlsanity.com/paper/2401.17791/) (2024)
- [Beyond the Known: Novel Class Discovery for Open-world Graph Learning](https://mlsanity.com/paper/2403.19907/) (2024)
- [Self-Supervised Deep Graph Embedding with High-Order Information Fusion for Community Discovery](https://mlsanity.com/paper/2102.03302/) (2021)
- [A Variational Graph Autoencoder for Manipulation Action Recognition and Prediction](https://mlsanity.com/paper/2110.13280/) (2021)
- [COmic: Convolutional Kernel Networks for Interpretable End-to-End Learning on (Multi-)Omics Data](https://mlsanity.com/paper/2212.02504/) (2022)
- [Fisher Information Embedding for Node and Graph Learning](https://mlsanity.com/paper/2305.07580/) (2023)

## Abstract (arXiv)

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing graphs as a sequence of kernel feature maps, where each node carries information about local graph substructures. On the one hand, the kernel point of view offers an unsupervised, expressive, and easy-to-regularize data representation, which is useful when limited samples are available. On the other hand, our model can also be trained end-to-end on large-scale data, leading to new types of graph convolutional neural networks. We show that our method achieves competitive performance on several graph classification benchmarks, while offering simple model interpretation. Our code is freely available at https://github.com/claying/GCKN.