# A Learned Generalized Geodesic Distance Function-Based Approach for Node Feature Augmentation on Graphs

arXiv: https://arxiv.org/abs/2407.01194 · HTML: https://mlsanity.com/paper/2407.01194/

## Key facts

- Cited by 1 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 1 Jul 2024.

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

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [False Information on Web and Social Media: A Survey](https://mlsanity.com/paper/1804.08559/) (2018)
- [Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth](https://mlsanity.com/paper/2202.08789/) (2022)
- [Tukey Depths and Hamilton-Jacobi Differential Equations](https://mlsanity.com/paper/2104.01648/) (2021)
- [An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields](https://mlsanity.com/paper/1709.09235/) (2017)

## Built on by (most cited first, 1 of 1)

- [Diffusion on Graph: Augmentation of Graph Structure for Node Classification](https://mlsanity.com/paper/2503.12563/) (2025)

## Abstract (arXiv)

Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves generating node features by learning a generalized geodesic distance function through a training pipeline that incorporates training data, graph topology and the node content features. The strength of this method lies in the proven robustness of the generalized geodesic distances to noise and outliers. Our contributions encompass improved performance in node classification tasks, competitive results with state-of-the-art methods on real-world graph datasets, the demonstration of the learnability of parameters within the generalized geodesic equation on graph, and dynamic inclusion of new labels.