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Graph Neural Networks for Modelling Traffic Participant Interaction

Frederik Diehl, Thomas Brunner, Michael Truong Le, Alois Knoll

arXiv:1903.01254v2cs.LGstat.ML

TL;DR

Traffic prediction raises the open question of how to model interactions between participants. This paper represents traffic scenes as graphs and applies adapted GNNs; on a dataset with plentiful interaction, including interactions reduced prediction error by over 30% compared with the best baseline.

  • Problem

    A major open question in traffic prediction is how to model interaction between participants.

    Source: §I · p. 1

  • Method

    The paper represents vehicles as graph nodes and possible interactions as edges, then evaluates two adapted GNN models for prediction.

    Source: §I · p. 1, §VI · p. 6

  • Results

    Including interactions decreased prediction error by over 30% compared with the best baseline on a dataset with plentiful interaction, with no increase in error on a dataset with little interaction.

    Source: §VI · p. 6

  • Takeaways & Limitations

    The results support graph-based interaction modeling as a worthwhile addition to traffic-prediction systems.

    Source: §I · p. 1

    The work is a proof of concept, and integration with existing state-of-the-art methods, particularly RNNs, and automatically finding relevant interactions remain open tasks.

    Source: §VI · p. 6

Abstract

from arXiv · show

By interpreting a traffic scene as a graph of interacting vehicles, we gain a flexible abstract representation which allows us to apply Graph Neural Network (GNN) models for traffic prediction. These naturally take interaction between traffic participants into account while being computationally efficient and providing large model capacity. We evaluate two state-of-the art GNN architectures and introduce several adaptations for our specific scenario. We show that prediction error in scenarios with much interaction decreases by 30% compared to a model that does not take interactions into account. This suggests that interaction is important, and shows that we can model it using graphs. This makes GNNs a worthwhile addition to traffic prediction systems.

I. INTRODUCTION

The introduction frames interaction modeling as an open traffic-prediction question and proposes representing vehicles and their interactions as a graph for GNN prediction. The paper evaluates two GNNs and reports lower error when interaction is plentiful.

I. INTRODUCTION

  • Existing interaction representations either use participant representations or fixed environment representations, with the latter posing a harder learning problem and the former scaling with possible interactions and underspecifying the task.Participant representations also require a human to choose a useful representation.Source: §I · p. 1
  • Representing vehicles as graph nodes and possible interactions as edges yields a sparse, high-level traffic-scene representation for GNNs.The paper presents graph-based interaction modeling as a worthwhile addition to traffic prediction systems.Source: §I · p. 1
  • Prediction error decreases by 30% versus the baseline when interaction is plentiful, with no worse performance when interaction is little.The evaluation uses two real-world datasets and compares against three baseline models; computational complexity remains reasonable and scales linearly with interactions.Source: §I · p. 1
  • The paper evaluates two state-of-the-art GNN models, introduces adaptations, and studies graph-construction techniques and adaptations on two datasets.The introduction also notes that traffic-prediction algorithms vary with prediction timespan and computational resources.Source: §I · p. 1, §II · pp. 1–2

A. Traffic Prediction

The section surveys traffic-prediction approaches and environmental representations, emphasizing that many established methods do not explicitly model interactions. It presents graph representations as a way to represent vehicles and their interactions together.

A. Traffic Prediction

  • Traffic-prediction models are grouped into physics-based, maneuver-based, and interaction-aware approaches, with machine-learning methods spanning different complexities and goals.The cited machine-learning examples include feed-forward networks, recurrent networks, and imitation learning; their performance depends on environment representation.Source: A. Traffic Prediction · p. 2

1) Sensor-like representation:

  • Sensor-like representations can encode information about many vehicles at constant size, but require many pixels or lidar beams per vehicle and vehicle extraction from sensor data.They do not require expert knowledge to define features.Source: 1) Sensor-like representation · p. 2

2) Discrete object representation:

  • Discrete-object representations predict per car and encode interaction through selected features, but are limited by simplistic assumptions about interactions.Examples include distance and approach speed to a preceding vehicle or multiple preprocessed features.Source: 2) Discrete object representation · p. 2

B. Environmental Representation

  • Representing participants as graph nodes and interactions as edges lets a behavior-prediction model operate on the graph and produce predictions for each node.This representation is presented as a way to avoid several shortcomings of earlier environment representations.Source: 2) Discrete object representation · p. 2

III. TRAFFIC PARTICIPANT PREDICTION FROM A GRAPH

The paper uses graph neural networks for node-level traffic prediction, including GCNs and GATs. It describes GCN neighborhood aggregation and adapts the GCN to distinguish ego features, weight edges by distance, and use an independent feed-forward output layer.

III. TRAFFIC PARTICIPANT PREDICTION FROM A GRAPH

  • GCN layers apply shared operations across graph nodes, and the paper also evaluates GAT because it supports edge features.The section notes prior experimental results in which GCN performs well across a wide variety of tasks.Source: §III · p. 2, A. Graph Convolutional Networks · p. 2

1) The Base Model:

  • A GCN transformation uses the adjacency matrix with added self-connections, its degree vector, and a learnable weight matrix to update layer activations.The cited formulation is a first-order approximation of a localized spectral filter; its complexity scales linearly in the number of edges and the l-layer transformation covers the l-hop neighborhood.Source: 1) The Base Model:  · p. 2

2) Adaptations for the GCN:

  • The adapted GCN removes self-connections and adds a second weight matrix to transform ego-node features separately from neighbors.The authors report that treating ego features like neighbor features appeared to obstruct prediction performance.Source: 2) Adaptations for the GCN · pp. 2–3
  • The GCN adaptations evaluate inverse-distance edge weights with self-loops set to 1 and replace the output layer with a node-wise feed-forward layer.The feed-forward output separates feature extraction in earlier GCN layers from the final prediction.Source: 2) Adaptations for the GCN · p. 3

B. Graph Attention Networks

The GAT computes node representations using attention over neighboring nodes. Its learned attention coefficients weight neighbor features, and multi-head attention combines differently parameterized mechanisms.

B. Graph Attention Networks

1) The Base Model:

  • The attention-weighted neighbor features are combined and passed through a non-linearity, usually ReLU.The layer’s node feature vector is formed from the weighted neighbor representations.Source: 1) The Base Model · p. 3
  • Multi-head attention uses differently parameterized mechanisms whose outputs are concatenated, or averaged in the last layer, and GAT complexity scales linearly with edges.The heads can create features from different subsets of nodes.Source: 1) The Base Model · p. 3

2) Adaptations for the GAT:

The GAT adaptations add edge features to attention and separately evaluate an ego-feature transformation, while retaining a feed-forward output layer.

2) Adaptations for the GAT:

  • Edge features, including relative positions, augment attention, and the relative positions are reused at each layer rather than learned as successive edge features.The base GAT attention depends only on the features of the two nodes.Source: 2) Adaptations for the GAT · p. 3
  • An explicit transformation of the ego node’s features is evaluated alongside the GAT’s attention mechanism.The authors note that attention could learn to concentrate a head on the ego node, but also test adding the transformation directly.Source: 2) Adaptations for the GAT · p. 3
  • The final prediction is produced by a feed-forward layer, as in the GCN adaptation.The GCN feed-forward output operates independently on each node’s features, decoupling feature extraction from prediction.Source: 2) Adaptations for the GAT · p. 3

C. Graph and Feature Construction

The section outlines fixed graph-connection strategies and an experiment design for testing graph models on NGSIM and HighD traffic data.

C. Graph and Feature Construction

  • The four fixed connection strategies are self-loops, all-vehicle connections, predecessor-only connections, and connections to up to eight nearby vehicles.The authors leave learned connection strategies and the necessary neighborhood size for future work; learning connections is described as difficult and quadratic in the number of vehicles.Source: C. Graph and Feature Construction · p. 3

IV. EXPERIMENTS

  • The experiments use real-world traffic data and keep models and baselines simple to isolate whether graph interpretation is beneficial.The stated questions concern necessary GNN adaptations, graph construction, and whether graph models improve prediction quality; RNNs, simulation steps, and imitation learning are excluded.Source: §IV · p. 3

A. Datasets

  • The evaluation uses the NGSIM I-80 dataset and the HighD dataset.The passages identify these two datasets as the experiment sources.Source: A. Datasets · p. 3

1) NGSIM:

  • NGSIM I-80 covers highway merging in three 15-minute recordings; trajectories are smoothed, sampled at 1 FPS, and split into five-second input and prediction intervals.Two recordings train the model, while the third is divided equally into validation and test sets; positions are smoothed over 0.5 seconds and velocities are computed from them.Source: 1) NGSIM · p. 4

2) HighD:

The section describes HighD data, the baseline comparisons, and the constant-velocity and Intelligent Driver Model baselines.

2) HighD:

  • HighD contains 16.5 hours of drone-recorded Autobahn data covering 110,000 vehicles and 45,000 km, but only about 5% of cars change lanes.Recordings are split by recording, with the last 10% held out for testing and the preceding 10% for validation.Source: 2) HighD · p. 4

B. Baselines

  • The approach is compared with two static model-based approaches and one learned approach; the constant-velocity model continues each car’s lateral and longitudinal velocity.The CVM extrapolates motion from the last observed frame.Source: B. Baselines · p. 4, 1) Constant Velocity Model (CVM) · p. 4

2) Intelligent Driver Model (IDM):

  • The IDM predicts longitudinal velocity changes using free-road and interaction acceleration, while assuming no lateral motion.Its tunable parameters include maximum acceleration, acceleration exponent, desired velocity, minimum front-vehicle distance, time gap, and maximum deceleration.Source: 2) Intelligent Driver Model (IDM) · p. 4
  • IDM parameters come from Morton et al. for NGSIM and are tuned for HighD using guided random search over 20,000 samples.The optimized parameter values are listed in Table I.Source: 2) Intelligent Driver Model (IDM) · p. 4, Table I · p. 4

3) Independent Feed-Forward Model:

An ego-only feed-forward model serves as a baseline for measuring the contribution of interaction; the section also specifies shared model configuration and error metrics.

3) Independent Feed-Forward Model:

  • The independent feed-forward model predicts trajectories from only the ego vehicle’s past data, providing a baseline for measuring gains from interaction.Source: 3) Independent Feed-Forward Model · p. 4

C. Model Configuration

  • Models use two 256-dimensional feature layers and a feed-forward output; the GAT uses four 64-dimensional attention heads, and two GNN layers give a two-hop receptive field.Inputs and outputs use fixed-length timesteps without recurrence, and training minimizes mean squared error over predicted displacements relative to the last position.Source: C. Model Configuration · p. 4

D. Performance Measure

  • Performance is measured by mean displacement over five seconds and final displacement after five seconds.Mean displacement weights each timestep identically.Source: D. Performance Measure · p. 4

E. Experimental Procedure

The evaluation examines GNN adaptations and graph-construction strategies through repeated experiments, then tests whether interaction graphs improve prediction. Removing residual connections and adding relative-position edge features yielded reported performance gains.

E. Experimental Procedure

  • Evaluations used ten random seeds and reported mean ± standard deviation.Figures show individual results and their overall distributions; the starred case used three evaluations.Source: E. Experimental Procedure · pp. 4–5

V. DISCUSSION

  • The evaluation asks whether architectural adaptations help, which graph construction to prefer, and whether interaction-graph information improves performance.Source: §V · p. 5

A. Which of our adaptions to GNNs are necessary?

  • At least 20% lower prediction error followed removing residual connections in both models; a feed-forward output layer slightly improved performance and stabilized training.Source: A. Which of our adaptions to GNNs are… · p. 5
  • About a meter lower final displacement came from adding relative-position edge features to GAT; edge weights slightly decreased GCN performance, especially without residual weights.The authors suggest residual weights model the distinction between ego and surrounding vehicles more effectively.Source: A. Which of our adaptions to GNNs are… · p. 5

B. How do we construct an interaction graph?

The paper compares interaction-graph construction strategies and evaluates whether graph models improve prediction. Neighbour-Connection performed best among the tested strategies, while the NGSIM results favored GNNs over the learning baseline.

B. How do we construct an interaction graph?

1) NGSIM:

  • 30% lower prediction error than the FF baseline was reported for GAT with fixed edge features on NGSIM; the reported figure and table cover the model comparisons.Every GNN model performed better than the baseline.Source: 1) NGSIM · p. 5

2) HighD:

The graph-based approach improves prediction when interaction is plentiful and retains performance when it is scarce. On HighD, where interaction is limited, learned models perform similarly; the paper also identifies further work needed to extend this proof of concept.

2) HighD:

  • On HighD, learned models show no significant performance difference; the authors attribute this to little interaction between cars.With little interaction, learned models degenerate to the noninteraction case, and the CVM interaction term becomes irrelevant.Source: 2) HighD · pp. 5–6, Figure 3 · p. 6
  • Several model changes and a good interaction-graph construction strategy improve performance.Source: 2) HighD · p. 6

VI. CONCLUSION

  • The paper models traffic scenes as graphs of interacting vehicles and evaluates two computationally efficient GNNs adapted to the prediction scenario.The graph represents vehicles as nodes and possible interactions as edges.Source: §VI · p. 6
  • Over 30%, prediction error decreased in a dataset with plentiful interaction compared with the best baseline model.The paper reports no increase in prediction error on a dataset with little interaction.Source: §VI · p. 6
  • The work is a proof of concept for graph-based interaction modelling as one technique for one aspect of traffic prediction.Integration with state-of-the-art methods, particularly RNNs, and automatic discovery of relevant interactions remain open tasks.Source: §VI · p. 6

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