Adaptive Trajectory Prediction via Transferable GNN

Yi XuLichen WangYizhou WangYun Fu

article2022CVPR105 citations

Proposes a transferable graph neural network framework that aligns feature distributions across disparate environments to prevent performance drops in cross-domain pedestrian trajectory forecasting.

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Accurately predicting pedestrian movement is essential for safety, navigation, and automated planning in autonomous driving and robotics. Current prediction systems typically assume that pedestrian movement patterns observed during training will match those encountered during real-world deployment. In practice, however, pedestrian density, walking speeds, and acceleration vary dramatically across different physical environments, such as open streets versus crowded university plazas. This environmental mismatch creates a domain shift problem that severely degrades the accuracy of standard predictive models.

The article demonstrates this vulnerability across standard benchmarks and introduces a new predictive framework called the Transferable Graph Neural Network to overcome it. The primary objective is to evaluate whether integrating unsupervised domain adaptation directly into a network can bridge distribution gaps and generate reliable pedestrian trajectory predictions in new, unseen target environments.

To evaluate this framework, the authors designed a transfer-learning benchmark across five real-world pedestrian datasets: ETH, Hotel, University, Zara1, and Zara2. This benchmark generated 20 cross-scene prediction tasks where models trained on one source environment were required to adapt to a distinct target environment. The framework uses graph neural network layers to capture spatial relationships and pedestrian interactions, combines them with an attention mechanism to extract fine-grained, individual-level movement features, and aligns source and target feature distributions using a distance-minimizing alignment loss. Crucially, the model accesses only the past observed trajectory history of the new target scene without requiring future trajectory labels, reflecting realistic deployment constraints.

The experimental findings show substantial improvements over existing techniques. Across all 20 cross-domain tasks, the proposed framework achieved an average prediction error of 0.96 meters and a final endpoint error of 1.82 meters, consistently outperforming five leading baseline models. Compared to top-performing baselines like Social-STGCNN, SGCN, and PECNet, the framework reduced average trajectory error by approximately 21.3% and final displacement error by roughly 20.5%. Furthermore, ablation tests confirmed that incorporating an individual-level attention module and explicit domain alignment significantly outperforms simply pooling features or training models on mixed datasets without alignment.

These findings have direct operational and safety implications for autonomous vehicles and mobile robotics. High prediction error in unfamiliar surroundings increases collision risks, delays vehicle decision-making, and limits operational scalability. The results show that deploying models naively across disparate environments without domain alignment introduces severe bias, whereas an adaptive framework allows systems to transfer learned motion dynamics to new operating domains without costly, manual retraining or ground-truth data collection.

Organizations developing autonomous navigation systems should adopt domain-invariant learning frameworks to make predictive models resilient to environmental shifts. Development teams should prioritize fine-grained individual feature alignment over standard sample-level domain adaptation techniques. Before deploying these models into safety-critical operations, organizations should conduct pilot trials in edge-case environments characterized by extreme crowd densities or non-standard movement dynamics to validate operational safety thresholds.

While the evaluation provides high confidence across standard cross-scene benchmarks, the scope of the evaluation relies on five public surveillance-style datasets with specific observation-to-prediction ratios. Readers should account for uncertainties in unseen edge environments that may feature significantly more complex occlusions, high vehicle-pedestrian mixed traffic, or sensor noise not present in these standard datasets.

Northeastern University Adaptive Trajectory Prediction Transferable Graph Neural Network pedestrian trajectory prediction

arXiv: 2203.05046

Paper: Social LSTM: Human Trajectory Prediction in Crowded Spaces, Alexandre Alahi et al. (2016). Introduces the foundational Social LSTM pooling architecture on the ETH and UCY datasets that established multi-pedestrian interaction modeling for trajectory forecasting.
Paper: Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks, Agrim Gupta et al. (2018). Pioneers generative multi-agent trajectory prediction with global pooling mechanisms, serving as a core baseline and architectural precursor for interaction-aware motion modeling.
Paper: Trajectron++: Dynamically-Feasible Trajectory Forecasting with Heterogeneous Data, Tim Salzmann et al. (2020). Formulates multi-agent trajectory forecasting on spatiotemporal graphs across standard pedestrian benchmarks, establishing key graph-based motion modeling principles.
Book: Domain-Adversarial Training of Neural Networks, Yaroslav Ganin et al. (2016). Establishes the fundamental domain-adversarial framework for learning domain-invariant feature representations under unsupervised domain shift.
Paper: You'll never walk alone: Modeling social behavior for multi-target tracking, S. Pellegrini et al. (2009). Provides the original ETH pedestrian dataset and interaction models that form the standard cross-domain evaluation benchmark used in the source paper.
Paper: Maximum Classifier Discrepancy for Unsupervised Domain Adaptation, Kuniaki Saito et al. (2017). Introduces decision boundary-based unsupervised domain adaptation, providing essential theoretical and methodological context for feature distribution alignment.
Paper: Spatio-temporal Graph Convolutional Neural Network: A Deep Learning Framework for Traffic Forecasting, Bing Yu et al. (2017). Introduces spatiotemporal graph convolutional networks for forecasting structured relational dynamics, providing the architectural foundation for subsequent GNN predictors.
Paper: Deep Domain Confusion: Maximizing for Domain Invariance, Eric Tzeng et al. (2014). Demonstrates how to optimize deep neural representations for domain invariance via explicit distribution alignment loss functions.

Paper: EqMotion: Equivariant Multi-Agent Motion Prediction with Invariant Interaction Reasoning, Chenxin Xu et al. (2023). Extends multi-agent trajectory forecasting by embedding geometric equivariance and invariant interaction reasoning directly into the sequence-to-sequence motion network.
Paper: Planning-oriented Autonomous Driving, Yi Hu et al. (2022). Integrates multi-agent motion forecasting into a comprehensive end-to-end framework that directly coordinates prediction with vehicle planning.
Paper: Trajectory-guided Control Prediction for End-to-end Autonomous Driving: A Simple yet Strong Baseline, Penghao Wu et al. (2022). Applies predicted trajectories to guide closed-loop control and vehicle actuation for robust end-to-end autonomous driving.
Paper: Generating Useful Accident-Prone Driving Scenarios via a Learned Traffic Prior, Davis Rempe et al. (2022). Leverages graph-based multi-agent motion priors to generate safety-critical adversarial scenarios for stress-testing autonomous vehicle planners.

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Abstract

Pedestrian trajectory prediction is an essential component in a wide range of AI applications such as autonomous driving and robotics. Existing methods usually assume the training and testing motions follow the same pattern while ignoring the potential distribution differences (e.g., shopping mall and street). This issue results in inevitable performance decrease. To address this issue, we propose a novel Transferable Graph Neural Network (T-GNN) framework, which jointly conducts trajectory prediction as well as domain alignment in a unified framework. Specifically, a domain-invariant GNN is proposed to explore the structural motion knowledge where the domain-specific knowledge is reduced. Moreover, an attention-based adaptive knowledge learning module is further proposed to explore fine-grained individual-level feature representations for knowledge transfer. By this way, disparities across different trajectory domains will be better alleviated. More challenging while practical trajectory prediction experiments are designed, and the experimental results verify the superior performance of our proposed model. To the best of our knowledge, our work is the pioneer which fills the gap in benchmarks and techniques for practical pedestrian trajectory prediction across different domains.

Keywords

Adaptive Trajectory Prediction Transferable Graph Neural Network pedestrian trajectory prediction deep unsupervised domain adaptation human trajectory forecasting transfer learning spatial-temporal feature representations autonomous driving SGCN models

1. Introduction
2. Related Works
2.1. Forecasting Pedestrian Trajectory
2.2. Graph-Involved Forecasting Models
2.3. Domain Adaptation
3. Our Method
3.1. Problem Definition
3.2. Spatial-Temporal Feature Representations
3.3. Attention-Based Adaptive Learning
3.4. Temporal Prediction Module
3.5. Objective Function
4. Experiments
4.1. Quantitative Analysis
4.2. Ablation Study
5. Conclusion
References

Knowls

Knowl 1 — Transferable Graph Neural Network Framework for Cross-Domain Trajectory Prediction
model/method
The Transferable Graph Neural Network (T-GNN) framework performs pedestrian trajectory forecasting under domain shift between a source domain (with $N_s$ pedestrians) and an unlabelled target domain (with $N_t$ pedestrians). Given observed pedestrian trajectories $\Gamma = \{\Gamma^1, \dots, \Gamma^N\}$ from time step $t = 1$ to $T_{obs}$ , where each pedestrian's trajectory is $\Gamma^i = \{o_1^i, \dots, o_{obs}^i\}$ with coordinates $o_t^i = (x_t^i, y_t^i) \in \mathbb{R}^2$ , the model forecasts future trajectories $\bar{\Gamma} = \{\bar{\Gamma}^1, \dots, \bar{\Gamma}^N\}$ from $t = T_{obs}+1$ to $T_{pred}$ , where $\bar{\Gamma}^i = \{o_{obs+1}^i, \dots, o_{pred}^i\}$ .

T-GNN unifies trajectory forecasting and unsupervised domain adaptation through three interacting components:
1. A weight-shared Spatial-Temporal Graph Neural Network (GCN) that constructs dynamic graphs for source and target scenes, extracting spatial-temporal feature matrices $F_{(s)} \in \mathbb{R}^{N_s \times D_f \times L_{obs}}$ and $F_{(t)} \in \mathbb{R}^{N_t \times D_f \times L_{obs}}$ , where $D_f$ is feature dimension and $L_{obs} = T_{obs}$ is the observation length.
2. An Attention-Based Adaptive Knowledge Learning Module that collapses individual pedestrian representations into domain-level context vectors $c_{(s)}, c_{(t)} \in \mathbb{R}^{D_v}$ (with $D_v = D_f \times L_{obs}$ ) using attention weights, allowing computation of a distribution alignment loss $\mathcal{L}_{align}$ despite variable pedestrian counts ( $N_s \neq N_t$ ).
3. A Temporal Prediction Module based on Temporal Convolutional Networks (TCN) that maps source features $F_{(s)}$ to future trajectory distributions parameterized as bivariate Gaussians, optimized via a prediction loss $\mathcal{L}_{pre}$ .
The entire network is trained end-to-end by jointly minimizing the weighted multi-task objective $\mathcal{L} = \mathcal{L}_{pre} + \lambda \mathcal{L}_{align}$ .
Knowl 2 — Spatial-Temporal Feature Representation with Dynamic Graph Attention and GCN
model/method
To extract spatial-temporal interaction features across pedestrians while eliminating scene size biases, T-GNN employs coordinate decentralization, dynamic graph attention, and cascaded graph convolutions.
1. Coordinate Decentralization: Coordinates of all $N$ pedestrians in a scene are normalized relative to the mean position at the final observed frame $T_{obs}$ : ${o'}_t^i = o_t^i - \frac{1}{N}\sum_{i=1}^N o_{obs}^i$ where ${o'}_t^i = ({x'}_t^i, {y'}_t^i)$ are relative coordinates.
2. Graph Construction and Feature Embedding: At time step $t$ , the graph $G_t = (V_t, E_t, F_t)$ consists of vertices $V_t = \{v_{t; i} \mid i = 1, \dots, N\}$ , feature matrix $F_t = \{f_{t; i} \mid i = 1, \dots, N\} \in \mathbb{R}^{N \times D_f}$ with embeddings $f_{t; i} = \sigma(({x'}_t^i, {y'}_t^i) W_o)$ (where $W_o \in \mathbb{R}^{2 \times D_f}$ is a learnable projection matrix and $\sigma(\cdot)$ is the ReLU activation function), and adjacency matrix $A_t = \{a_{t; i,j}\} \in \mathbb{R}^{N \times N}$ initialized with pairwise Euclidean distances: $a_{t; i,j} = \|{o'}_t^i - {o'}_t^j\|_2$
3. Dynamic Graph Attention Layer (GAL): Dynamic spatial relations are updated via graph attention coefficients $\alpha_{t; i, j}$ : $\alpha_{t; i,j} = \frac{\exp\left(\phi\left(W_l [a_{t; i} \oplus a_{t; j}]\right)\right)}{\sum_{j=1}^N \exp\left(\phi\left(W_l [a_{t; i} \oplus a_{t; j}]\right)\right)}$ where $a_{t; i} \in \mathbb{R}^{N \times 1}$ is the $i$ -th column of $A_t$ , $\oplus$ is row concatenation, $W_l \in \mathbb{R}^{1 \times 2N}$ is a learnable parameter vector, and $\phi(\cdot)$ is LeakyReLU with negative slope $\theta = 0.2$ . The updated adjacency column is $p_{t; i} = \sigma\left(\sum_{j=1}^N \alpha_{t; i, j} a_{t; j}\right)$ , yielding updated adjacency matrix $A'_t \in \mathbb{R}^{N \times N}$ .
4. Spatial-Temporal Graph Convolution: Self-loops are added via $\hat{A}_t = A'_t + I$ . Stacking across observation steps $t = 1, \dots, T_{obs}$ forms $\hat{A} = \{\hat{A}_1, \dots, \hat{A}_{obs}\} \in \mathbb{R}^{N \times N \times L_{obs}}$ and degree matrices $\hat{D} = \{\hat{D}_1, \dots, \hat{D}_{obs}\}$ . The $l$ -th GCN layer output is computed as: $F^{(l+1)} = \sigma\left(\hat{D}^{-\frac{1}{2}} \hat{A} \hat{D}^{-\frac{1}{2}} F^{(l)} W^{(l)}\right)$ where $W^{(l)}$ are trainable parameters. Three cascaded GCN layers ( $l = 3$ ) extract final spatial-temporal representation matrices $F_{(s)} \in \mathbb{R}^{N_s \times D_f \times L_{obs}}$ and $F_{(t)} \in \mathbb{R}^{N_t \times D_f \times L_{obs}}$ for source and target scenes.
Knowl 3 — Attention-Based Individual-Level Domain Alignment Module
model/method
In cross-domain trajectory prediction, standard domain adaptation methods cannot align global scene representations directly because the number of pedestrians $N_s$ in the source domain and $N_t$ in the target domain vary per frame. The attention-based adaptive knowledge learning module overcomes this misalignment by computing individual-level attention weights over pedestrian trajectories to form domain context vectors.

Feature maps $F_{(s)} \in \mathbb{R}^{N_s \times D_f \times L_{obs}}$ and $F_{(t)} \in \mathbb{R}^{N_t \times D_f \times L_{obs}}$ are reformatted into collections of pedestrian vectors: $F_{(s)} = [f_1^{(s)}, f_2^{(s)}, \dots, f_{N_s}^{(s)}], \quad f_i^{(s)} \in \mathbb{R}^{D_v}$ $F_{(t)} = [f_1^{(t)}, f_2^{(t)}, \dots, f_{N_t}^{(t)}], \quad f_i^{(t)} \in \mathbb{R}^{D_v}$ where $D_v = D_f \times L_{obs}$ , $D_f$ is feature dimensionality, and $L_{obs}$ is observation length.

Individual representativeness scores $\beta_i^{(s)}$ and $\beta_i^{(t)}$ within their respective domains are computed using shared parameters $h \in \mathbb{R}^{D_v}$ and $W_f \in \mathbb{R}^{D_v \times D_v}$ : $\beta_i^{(s)} = \frac{\exp\left(h^\top \tanh\left(W_f f_i^{(s)}\right)\right)}{\sum_{j=1}^{N_s} \exp\left(h^\top \tanh\left(W_f f_j^{(s)}\right)\right)}$ $\beta_i^{(t)} = \frac{\exp\left(h^\top \tanh\left(W_f f_i^{(t)}\right)\right)}{\sum_{j=1}^{N_t} \exp\left(h^\top \tanh\left(W_f f_j^{(t)}\right)\right)}$

The refined domain-level context vectors $c_{(s)}, c_{(t)} \in \mathbb{R}^{D_v}$ are weighted sums over pedestrians: $c_{(s)} = \sum_{i=1}^{N_s} \beta_i^{(s)} f_i^{(s)}, \quad c_{(t)} = \sum_{i=1}^{N_t} \beta_i^{(t)} f_i^{(t)}$

The distribution alignment loss $\mathcal{L}_{align}$ is calculated as the normalized squared $L_2$ distance between context vectors: $\mathcal{L}_{align} = \frac{1}{D_f} \|c_{(s)} - c_{(t)}\|_2^2$
Knowl 4 — Temporal Prediction Module and Bi-variate Gaussian Training Objective
model/method
The temporal prediction module generates future trajectories from source domain feature representations $F_{(s)} \in \mathbb{R}^{N_s \times D_f \times L_{obs}}$ using Temporal Convolutional Networks (TCN) along the temporal dimension, avoiding sequential RNN error accumulation and gradient vanishing.

The layer-wise operation across three cascaded TCN layers ( $l = 3$ ) is: $F_{(s)}^{(l+1)} = \text{TCN}\left(F_{(s)}^{(l)}; W_t^{(l)}\right)$ where $W_t^{(l)}$ denotes trainable parameters, producing prediction features $F_{(s), pred} \in \mathbb{R}^{N_s \times D_f \times L_{pred}}$ , with $L_{pred} = T_{pred} - T_{obs}$ .

A linear layer parameterizes a bivariate Gaussian distribution for each pedestrian $i$ at future time step $t \in \{T_{obs}+1, \dots, T_{pred}\}$ : $(\hat{\mu}_t^i, \hat{\sigma}_t^i, \hat{\rho}_t^i) = \text{Linear}\left(F_{(s), pred}; W_p\right)$ where $\hat{\mu}_t^i = (\hat{\mu}_x, \hat{\mu}_y)_t^i$ is the predicted mean position, $\hat{\sigma}_t^i = (\hat{\sigma}_x, \hat{\sigma}_y)_t^i$ represents standard deviations, and $\hat{\rho}_t^i$ is the cross-coordinate correlation coefficient. Future pedestrian positions are modeled as $(x_t^i, y_t^i) \sim \mathcal{N}(\hat{\mu}_t^i, \hat{\sigma}_t^i, \hat{\rho}_t^i)$ .

The trajectory prediction loss $\mathcal{L}_{pre}$ is the negative log-likelihood of ground-truth future positions: $\mathcal{L}_{pre} = -\sum_{t=T_{obs}+1}^{T_{pred}} \log P\left((x_t^i, y_t^i) \mid \hat{\mu}_t^i, \hat{\sigma}_t^i, \hat{\rho}_t^i\right)$

The total training loss jointly optimizes prediction accuracy on the source domain and feature alignment between source and target domains: $\mathcal{L} = \mathcal{L}_{pre} + \lambda \mathcal{L}_{align}$ where $\lambda$ balances prediction and alignment losses (set empirically to $\lambda = 1$ ).
Knowl 5 — Cross-Domain Trajectory Prediction Benchmark and Evaluation Protocol
experimental setup
The cross-domain trajectory prediction benchmark evaluates models under distribution shifts across five real-world scenes from the ETH dataset (ETH, HOTEL) and UCY dataset (UNIV, ZARA1, ZARA2), denoted as domains A, B, C, D, and E.

Experimental Tasks: Each scene serves as a distinct domain, creating 20 directional cross-domain transfer tasks: $A \to \{B, C, D, E\}$ , $B \to \{A, C, D, E\}$ , $C \to \{A, B, D, E\}$ , $D \to \{A, B, C, E\}$ , and $E \to \{A, B, C, D\}$ .

Evaluation Protocol: For a task $S \to T$ (source $S$ , target $T$ ):
- Standard baselines are trained on the training set of $S$ concatenated with the validation set of $T$ .
- Unsupervised domain adaptation models (including T-GNN) are trained on the training set of $S$ (with full trajectory labels) and only the observed trajectory history ( $T_1$ to $T_{obs}$ ) of the validation set of $T$ (without access to target future trajectories during training).
- All models are evaluated exclusively on the independent, non-overlapping testing set of $T$ .
Configuration and Hyperparameters:
- Observation horizon: $L_{obs} = 8$ frames; prediction horizon: $L_{pred} = 12$ frames.
- Network structure: 3 GCN layers, 3 TCN layers, feature dimension $D_f = 64$ , batch size 16, alignment trade-off parameter $\lambda = 1$ .
- Training: Adam optimizer for 200 epochs with initial learning rate 0.001, decayed to 0.0005 at epoch 100.
- Inference: 20 trajectory samples are generated per pedestrian; the best-of-20 prediction is evaluated.
Evaluation Metrics:
- Average Displacement Error (ADE): $\text{ADE} = \frac{\sum_{i=1}^{N_t} \sum_{t=T_{obs}+1}^{T_{pred}} \|\hat{o}_t^i - o_t^i\|_2}{N_t(T_{pred} - T_{obs})}$
- Final Displacement Error (FDE): $\text{FDE} = \frac{\sum_{i=1}^{N_t} \|\hat{o}_{pred}^i - o_{pred}^i\|_2}{N_t}$ where $N_t$ is total pedestrians in the target domain, $\hat{o}_t^i$ is predicted position, and $o_t^i$ is ground truth.

Knowl 6 — Accuracy Comparison Across 20 Cross-Domain Trajectory Prediction Tasks

data/table

Performance of T-GNN compared to five baseline models (Social-STGCNN, PECNet, RSBG, Tra2Tra, SGCN) across all 20 cross-domain transfer tasks evaluated on the ETH/UCY datasets (A: ETH, B: HOTEL, C: UNIV, D: ZARA1, E: ZARA2) using Average Displacement Error (ADE) and Final Displacement Error (FDE) in meters.

Method	A2B	A2C	A2D	A2E	B2A	B2C	B2D	B2E	C2A	C2B	C2D	C2E	D2A	D2B	D2C	D2E	E2A	E2B	E2C	E2D	Ave
Average Displacement Error (ADE, meters)
Social-STGCNN	1.83	1.58	1.30	1.31	3.02	1.38	2.63	1.58	1.16	0.70	0.82	0.54	1.04	1.05	0.73	0.47	0.98	1.09	0.74	0.50	1.22
PECNet	1.97	1.68	1.24	1.35	3.11	1.35	2.69	1.62	1.39	0.82	0.93	0.57	1.10	1.17	0.92	0.52	1.01	1.25	0.83	0.61	1.31
RSBG	2.21	1.59	1.48	1.42	3.18	1.49	2.72	1.73	1.23	0.87	1.04	0.60	1.19	1.21	0.80	0.49	1.09	1.37	1.03	0.78	1.38
Tra2Tra	1.72	1.58	1.27	1.37	3.32	1.36	2.67	1.58	1.16	0.70	0.85	0.60	1.09	1.07	0.81	0.52	1.03	1.10	0.75	0.52	1.25
SGCN	1.68	1.54	1.26	1.28	3.22	1.38	2.62	1.58	1.14	0.70	0.82	0.52	1.05	0.97	0.80	0.48	0.97	1.08	0.75	0.51	1.22
T-GNN (Ours)	1.13	1.25	0.94	1.03	2.54	1.08	2.25	1.41	0.97	0.54	0.61	0.23	0.88	0.78	0.59	0.32	0.87	0.72	0.65	0.34	0.96
Final Displacement Error (FDE, meters)
Social-STGCNN	3.24	2.86	2.53	2.43	5.16	2.51	4.86	2.88	2.30	1.34	1.74	1.10	2.21	1.99	1.41	0.88	2.10	2.05	1.47	1.01	2.30
PECNet	3.33	2.83	2.53	2.45	5.23	2.48	4.90	2.86	2.22	1.32	1.68	1.12	2.20	2.05	1.52	0.88	2.10	1.84	1.45	0.98	2.29
RSBG	3.42	2.96	2.75	2.50	5.28	2.59	5.19	3.10	2.36	1.55	1.99	1.37	2.28	2.22	1.77	0.97	2.19	2.29	1.81	1.34	2.50
Tra2Tra	3.29	2.88	2.66	2.45	5.22	2.50	4.89	2.90	2.29	1.33	1.78	1.09	2.26	2.12	1.63	0.92	2.18	2.06	1.52	1.17	2.34
SGCN	3.22	2.81	2.52	2.40	5.18	2.47	4.83	2.85	2.24	1.32	1.71	1.03	2.23	1.90	1.48	0.97	2.10	1.95	1.52	0.99	2.29
T-GNN (Ours)	2.18	2.25	1.78	1.84	4.15	1.82	4.04	2.53	1.91	1.12	1.30	0.87	1.92	1.46	1.25	0.65	1.86	1.45	1.28	0.72	1.82

T-GNN consistently outperforms all competing baselines across every transfer task. Overall, T-GNN achieves an average ADE of 0.96 m (a 21.31% error reduction compared to Social-STGCNN and SGCN at 1.22 m) and an average FDE of 1.82 m (a 20.52% error reduction compared to PECNet and SGCN at 2.29 m).

Knowl 7 — Domain Discrepancy Statistics Across Trajectory Datasets

data/table

Statistical analysis across five pedestrian trajectory scenes demonstrates substantial domain gaps in crowd density, velocity, and acceleration patterns.

Metric	ETH	HOTEL	UNIV	ZARA1	ZARA2	E-D	S-D
NoS	70	301	947	602	921	877	383.63
NoP	181	1053	24334	2253	5833	24153	10073.07
AN	2.586	3.498	25.696	3.743	6.333	23.11	9.78
AV (m/s)	0.437	0.178	0.205	0.369	0.206	0.259	0.11
AA (m/s $^2$ )	0.131	0.060	0.035	0.039	0.026	0.105	0.04

Metric definitions:

NoS: number of trajectory sequences to be predicted.
NoP: total number of unique pedestrians across the scene.
AN: average number of pedestrians present in each sequence.
AV: average velocity of pedestrians per sequence in meters per second (m/s).
AA: average acceleration of pedestrians per sequence in meters per second squared (m/s $^2$ ).
E-D: extreme deviation (maximum minus minimum value across scenes).
S-D: standard deviation across scenes.

These statistics reveal significant domain disparities: pedestrian density (AN) in UNIV (25.696) is nearly $10\times$ that in ETH (2.586); mean velocity (AV) in ETH (0.437 m/s) is roughly $2.5\times$ higher than in HOTEL (0.178 m/s); and mean acceleration (AA) in ETH (0.131 m/s $^2$ ) is $5\times$ higher than in ZARA2 (0.026 m/s $^2$ ).

Knowl 8 — Comparison of Domain Adaptation Distance Measures for Trajectory Transfer

data/table

Average trajectory prediction performance (ADE / FDE in meters) across all 20 transfer tasks when varying the domain discrepancy alignment loss $\mathcal{L}_{align}$ within the T-GNN architecture.

Compared DA strategies:

T-GNN + MMD: Multi-Kernel Maximum Mean Discrepancies loss.
T-GNN + CORAL: Deep Correlation Alignment (Deep CORAL) loss.
T-GNN + GFK: Geodesic Flow Kernel domain adaptation strategy.
T-GNN + UDA: Unsupervised domain adaptive graph convolutional network using an adversarial domain discriminator loss.
T-GNN ( $L_2$ ): Normalized squared $L_2$ distance between attention-weighted context vectors $c_{(s)}$ and $c_{(t)}$ .

The attention-weighted $L_2$ distance achieves superior performance compared to distribution-matching and adversarial losses, indicating that individual-weighted feature representations better preserve the underlying spatial characteristics needed for trajectory forecasting.

Knowl 9 — Ablation Study on Architecture Components and Loss Balancing Weight

data/table

Ablation experiments evaluate the contribution of individual T-GNN components on five transfer tasks (A2B, B2C, C2D, D2E, E2A; A: ETH, B: HOTEL, C: UNIV, D: ZARA1, E: ZARA2) alongside the sensitivity of performance to the trade-off parameter $\lambda$ .

Component Variants:

T-GNN w/o GAL: Dynamic graph attention layer removed; adjacency attention $\alpha_{t; i, j}$ is static.
T-GNN w/o AAL w/ AP: Attention-based adaptive learning module replaced with average pooling across pedestrians.
T-GNN w/o AAL w/ LL: Attention-based adaptive learning module replaced with a single trainable linear layer.
Social-STGCNN-V1 / SGCN-V1 / T-GNN-V1: Trained purely on source data without target validation data or adaptation loss.
Social-STGCNN / SGCN / T-GNN-V2: Trained directly on mixed source and target validation data without domain adaptation.
T-GNN (Ours): Complete model with dynamic graph attention and attention-based context alignment.

Variants	ID	A2B	B2C	C2D	D2E	E2A
T-GNN w/o GAL	1	1.51 / 2.34	1.17 / 1.90	0.69 / 1.42	0.39 / 0.71	0.90 / 1.98
T-GNN w/o AAL w/ AP	2	1.78 / 2.85	1.23 / 2.02	0.77 / 1.53	0.42 / 0.79	0.96 / 2.03
T-GNN w/o AAL w/ LL	3	1.81 / 2.91	1.25 / 2.03	0.76 / 1.48	0.43 / 0.79	0.94 / 2.01
Social-STGCNN-V1	4	2.18 / 3.68	2.30 / 3.21	1.59 / 2.54	1.23 / 1.72	1.73 / 2.98
SGCN-V1	5	2.03 / 3.53	2.35 / 3.22	1.68 / 2.71	1.12 / 1.59	1.81 / 3.02
T-GNN-V1	6	2.12 / 3.58	2.28 / 3.21	1.73 / 2.76	1.19 / 1.58	1.74 / 2.95
Social-STGCNN	7	1.83 / 3.24	1.38 / 2.51	0.82 / 1.74	0.47 / 0.88	0.98 / 2.10
SGCN	8	1.68 / 3.24	1.38 / 2.47	0.82 / 1.71	0.48 / 0.97	0.97 / 2.10
T-GNN-V2	9	1.89 / 3.25	1.35 / 2.48	0.88 / 1.93	0.53 / 0.97	0.98 / 2.16
T-GNN (Ours)	10	1.13 / 2.18	1.08 / 1.82	0.61 / 1.30	0.32 / 0.65	0.87 / 1.86

Sensitivity to Alignment Weight $\lambda$ (Average across 20 tasks):

Removing graph attention (Variant 1) or substituting the adaptive attention learning module with average pooling (Variant 2) or a linear layer (Variant 3) causes substantial degradation. Setting $\lambda = 1.0$ yields optimal balance between trajectory prediction loss and domain alignment loss.

Coverage note — No substantial contributed material was omitted; all key architectural components, objectives, domain shift benchmarks, quantitative results, loss comparisons, and ablation studies are included.

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Citation

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Xu, Y., et al. “Adaptive Trajectory Prediction via Transferable GNN”. arXiv, 2022, http://arxiv.org/abs/2203.05046v2.

APA

Xu, Y., Wang, L., Wang, Y., & Fu, Y. (2022). Adaptive Trajectory Prediction via Transferable GNN. arXiv. http://arxiv.org/abs/2203.05046v2

Chicago

Xu, Y., L. Wang, Y. Wang, and Y. Fu. 2022. “Adaptive Trajectory Prediction via Transferable GNN”. arXiv. http://arxiv.org/abs/2203.05046v2.

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Xu, Y. et al. (2022) “Adaptive Trajectory Prediction via Transferable GNN”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2203.05046v2.

Vancouver

1. Xu Y, Wang L, Wang Y, Fu Y (2022) Adaptive Trajectory Prediction via Transferable GNN. arXiv

BibTeX

@article{xu2022adaptive,
  title = {Adaptive Trajectory Prediction via Transferable GNN},
  author = {Xu, Yi and Wang, Lichen and Wang, Yizhou and Fu, Yun},
  year = {2022},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2203.05046v2},
  eprint = {2203.05046}
}

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Method	Average ADE / FDE (m)
T-GNN + MMD	1.11 / 2.11
T-GNN + CORAL	1.07 / 2.01
T-GNN + GFK	1.15 / 2.08
T-GNN + UDA	1.07 / 2.09
T-GNN (Ours, $L_2$ context distance)	0.96 / 1.82

Metric	$\lambda = 0.01$	$\lambda = 0.1$	$\lambda = 1.0$	$\lambda = 5.0$	$\lambda = 10.0$
ADE (m)	1.19	1.05	0.96	1.16	1.31
FDE (m)	2.16	2.02	1.82	2.07	2.45

Adaptive Trajectory Prediction via Transferable GNN

Abstract

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Table of Contents

Knowls

Knowl 1 — Transferable Graph Neural Network Framework for Cross-Domain Trajectory Prediction

Knowl 2 — Spatial-Temporal Feature Representation with Dynamic Graph Attention and GCN

Knowl 3 — Attention-Based Individual-Level Domain Alignment Module

Knowl 4 — Temporal Prediction Module and Bi-variate Gaussian Training Objective

Knowl 5 — Cross-Domain Trajectory Prediction Benchmark and Evaluation Protocol

Knowl 6 — Accuracy Comparison Across 20 Cross-Domain Trajectory Prediction Tasks

Knowl 7 — Domain Discrepancy Statistics Across Trajectory Datasets

Knowl 8 — Comparison of Domain Adaptation Distance Measures for Trajectory Transfer

Knowl 9 — Ablation Study on Architecture Components and Loss Balancing Weight

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