# A Multidimensional Graph Fourier Transformation Neural Network for Vehicle Trajectory Prediction

arXiv: https://arxiv.org/abs/2305.07416 · HTML: https://mlsanity.com/paper/2305.07416/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 12 May 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [Multi-Head Attention for Multi-Modal Joint Vehicle Motion Forecasting](https://mlsanity.com/paper/1910.03650/) (2019)
- [Spectral Temporal Graph Neural Network for Trajectory Prediction](https://mlsanity.com/paper/2106.02930/) (2021)
- [Variational Autoencoder-Based Vehicle Trajectory Prediction with an Interpretable Latent Space](https://mlsanity.com/paper/2103.13726/) (2021)
- [Graph and Recurrent Neural Network-based Vehicle Trajectory Prediction For Highway Driving](https://mlsanity.com/paper/2107.03663/) (2021)
- [Multi-dimensional Graph Fourier Transform](https://mlsanity.com/paper/1712.07811/) (2017)

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

- [Reliable Trajectory Prediction and Uncertainty Quantification with Conditioned Diffusion Models](https://mlsanity.com/paper/2405.14384/) (2024)
- [Prediction and Interpretation of Vehicle Trajectories in the Graph Spectral Domain](https://mlsanity.com/paper/2309.16702/) (2023)
- [Optimization and Interpretability of Graph Attention Networks for Small Sparse Graph Structures in Automotive Applications](https://mlsanity.com/paper/2305.16196/) (2023)
- [Hybrid Machine Learning Model with a Constrained Action Space for Trajectory Prediction](https://mlsanity.com/paper/2501.03666/) (2025)
- [Assessing the Completeness of Traffic Scenario Categories for Automated Highway Driving Functions via Cluster-based Analysis](https://mlsanity.com/paper/2506.02599/) (2025)
- [X-TRACK: Physics-Aware xLSTM for Realistic Vehicle Trajectory Prediction](https://mlsanity.com/paper/2511.00266/) (2025)
- [Uncertainty-Aware Diffusion Model for Multimodal Highway Trajectory Prediction via DDIM Sampling](https://mlsanity.com/paper/2602.21319/) (2026)
- [FoSS: Modeling Long Range Dependencies and Multimodal Uncertainty in Trajectory Prediction via Fourier State Space Integration](https://mlsanity.com/paper/2603.01284/) (2026)

## Abstract (arXiv)

This work introduces the multidimensional Graph Fourier Transformation Neural Network (GFTNN) for long-term trajectory predictions on highways. Similar to Graph Neural Networks (GNNs), the GFTNN is a novel network architecture that operates on graph structures. While several GNNs lack discriminative power due to suboptimal aggregation schemes, the proposed model aggregates scenario properties through a powerful operation: the multidimensional Graph Fourier Transformation (GFT). The spatio-temporal vehicle interaction graph of a scenario is converted into a spectral scenario representation using the GFT. This beneficial representation is input to the prediction framework composed of a neural network and a descriptive decoder. Even though the proposed GFTNN does not include any recurrent element, it outperforms state-of-the-art models in the task of highway trajectory prediction. For experiments and evaluation, the publicly available datasets highD and NGSIM are used