# Graph Filtration Kernels

arXiv: https://arxiv.org/abs/2110.11862 · HTML: https://mlsanity.com/paper/2110.11862/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 22 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Relational Pooling for Graph Representations](https://mlsanity.com/paper/1903.02541/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [Tree-Sliced Variants of Wasserstein Distances](https://mlsanity.com/paper/1902.00342/) (2019)
- [Graph Neural Networks with Local Graph Parameters](https://mlsanity.com/paper/2106.06707/) (2021)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs](https://mlsanity.com/paper/2105.05911/) (2021)

## Built on by (most cited first, 8 of 8)

- [HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification](https://mlsanity.com/paper/2211.02904/) (2022)
- [Fast Graph Generation via Autoregressive Noisy Filtration Modeling](https://mlsanity.com/paper/2502.02415/) (2025)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Multi-scale Wasserstein Shortest-path Graph Kernels for Graph Classification](https://mlsanity.com/paper/2206.00979/) (2022)
- [AERK: Aligned Entropic Reproducing Kernels through Continuous-time Quantum Walks](https://mlsanity.com/paper/2303.03396/) (2023)
- [Revealing Combinatorial Reasoning of GNNs via Graph Concept Bottleneck Layer](https://mlsanity.com/paper/2603.02025/) (2026)
- [QESK: Quantum-based Entropic Subtree Kernels for Graph Classification](https://mlsanity.com/paper/2212.05228/) (2022)
- [Deep Hierarchical Graph Alignment Kernels](https://mlsanity.com/paper/2405.05545/) (2024)

## Abstract (arXiv)

The majority of popular graph kernels is based on the concept of Haussler's R-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering graph filtrations: Using meaningful orders on the set of edges, which allow to construct a sequence of nested graphs, we can consider a graph at multiple granularities. For one thing, this provides access to features on different levels of resolution. Furthermore, rather than to simply compare frequencies of features in graphs, it allows for their comparison in terms of when and for how long they exist in the sequences. In this work, we propose a family of graph kernels that incorporate these existence intervals of features. While our approach can be applied to arbitrary graph features, we particularly highlight Weisfeiler-Lehman vertex labels, leading to efficient kernels. We show that using Weisfeiler-Lehman labels over certain filtrations strictly increases the expressive power over the ordinary Weisfeiler-Lehman procedure in terms of deciding graph isomorphism. In fact, this result directly yields more powerful graph kernels based on such features and has implications to graph neural networks due to their close relationship to the Weisfeiler-Lehman method. We empirically validate the expressive power of our graph kernels and show significant improvements over state-of-the-art graph kernels in terms of predictive performance on various real-world benchmark datasets.