# Graph Classification Gaussian Processes via Hodgelet Spectral Features

arXiv: https://arxiv.org/abs/2410.10546 · HTML: https://mlsanity.com/paper/2410.10546/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Generalized Simplicial Attention Neural Networks](https://mlsanity.com/paper/2309.02138/) (2023)
- [Graph-based Semi-Supervised & Active Learning for Edge Flows](https://mlsanity.com/paper/1905.07451/) (2019)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (2023)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [Hodgelets: Localized Spectral Representations of Flows on Simplicial Complexes](https://mlsanity.com/paper/2109.08728/) (2021)
- [Weighted simplicial complexes and their representation power of higher-order network data and topology](https://mlsanity.com/paper/2207.04710/) (2022)
- [Topological Slepians: Maximally Localized Representations of Signals over Simplicial Complexes](https://mlsanity.com/paper/2210.14758/) (2022)
- [Graph Classification Gaussian Processes via Spectral Features](https://mlsanity.com/paper/2306.03770/) (2023)

## Built on by (most cited first, 3 of 3)

- [Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representations](https://mlsanity.com/paper/2505.10877/) (2025)
- [Measuring Structure in Graph Benchmark Datasets Using Graph Invariants](https://mlsanity.com/paper/2605.06462/) (2026)
- [Families of Optimal Transport Kernels for Cell Complexes](https://mlsanity.com/paper/2507.16569/) (2025)

## Abstract (arXiv)

The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into spectral features in the Euclidean domain, and using them as the input points of classical kernels. However, this approach currently only takes into account features on vertices, whereas some graph datasets also support features on edges. In this work, we present a Gaussian process-based classification algorithm that can leverage one or both vertex and edges features. Furthermore, we take advantage of the Hodge decomposition to better capture the intricate richness of vertex and edge features, which can be beneficial on diverse tasks.