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Unlocking Dynamic Inter-Client Spatial Dependencies: A Federated Spatio-Temporal Graph Learning Method for Traffic Flow Forecasting

Feng Wang, Tianxiang Chen, Shuyue Wei, Qian Chu, Yi Zhang, Yifan Sun, Zhiming Zheng

TL;DR

Traffic flow forecasting in federated settings suffers from dynamic inter-client spatial dependencies under data locality constraints. FedSTGD presents a TGCRN-based federated framework with three core components: federated nonlinear computation decomposition, graph node embedding augmentation, and a client-server collective learning protocol to reconstruct dynamic inter-client spatial dependencies. The approach enables privacy-preserving distributed computation and demonstrates superior performance over state-of-the-art baselines on four real-world datasets, closely matching centralized results; ablation and sensitivity analyses confirm the contributions and robustness of the framework. This work advances scalable, privacy-conscious TFF by effectively capturing evolving inter-client spatial dynamics across multiple stakeholders.

Abstract

Spatio-temporal graphs are powerful tools for modeling complex dependencies in traffic time series. However, the distributed nature of real-world traffic data across multiple stakeholders poses significant challenges in modeling and reconstructing inter-client spatial dependencies while adhering to data locality constraints. Existing methods primarily address static dependencies, overlooking their dynamic nature and resulting in suboptimal performance. In response, we propose Federated Spatio-Temporal Graph with Dynamic Inter-Client Dependencies (FedSTGD), a framework designed to model and reconstruct dynamic inter-client spatial dependencies in federated learning. FedSTGD incorporates a federated nonlinear computation decomposition module to approximate complex graph operations. This is complemented by a graph node embedding augmentation module, which alleviates performance degradation arising from the decomposition. These modules are coordinated through a client-server collective learning protocol, which decomposes dynamic inter-client spatial dependency learning tasks into lightweight, parallelizable subtasks. Extensive experiments on four real-world datasets demonstrate that FedSTGD achieves superior performance over state-of-the-art baselines in terms of RMSE, MAE, and MAPE, approaching that of centralized baselines. Ablation studies confirm the contribution of each module in addressing dynamic inter-client spatial dependencies, while sensitivity analysis highlights the robustness of FedSTGD to variations in hyperparameters.

Unlocking Dynamic Inter-Client Spatial Dependencies: A Federated Spatio-Temporal Graph Learning Method for Traffic Flow Forecasting

TL;DR

Traffic flow forecasting in federated settings suffers from dynamic inter-client spatial dependencies under data locality constraints. FedSTGD presents a TGCRN-based federated framework with three core components: federated nonlinear computation decomposition, graph node embedding augmentation, and a client-server collective learning protocol to reconstruct dynamic inter-client spatial dependencies. The approach enables privacy-preserving distributed computation and demonstrates superior performance over state-of-the-art baselines on four real-world datasets, closely matching centralized results; ablation and sensitivity analyses confirm the contributions and robustness of the framework. This work advances scalable, privacy-conscious TFF by effectively capturing evolving inter-client spatial dynamics across multiple stakeholders.

Abstract

Spatio-temporal graphs are powerful tools for modeling complex dependencies in traffic time series. However, the distributed nature of real-world traffic data across multiple stakeholders poses significant challenges in modeling and reconstructing inter-client spatial dependencies while adhering to data locality constraints. Existing methods primarily address static dependencies, overlooking their dynamic nature and resulting in suboptimal performance. In response, we propose Federated Spatio-Temporal Graph with Dynamic Inter-Client Dependencies (FedSTGD), a framework designed to model and reconstruct dynamic inter-client spatial dependencies in federated learning. FedSTGD incorporates a federated nonlinear computation decomposition module to approximate complex graph operations. This is complemented by a graph node embedding augmentation module, which alleviates performance degradation arising from the decomposition. These modules are coordinated through a client-server collective learning protocol, which decomposes dynamic inter-client spatial dependency learning tasks into lightweight, parallelizable subtasks. Extensive experiments on four real-world datasets demonstrate that FedSTGD achieves superior performance over state-of-the-art baselines in terms of RMSE, MAE, and MAPE, approaching that of centralized baselines. Ablation studies confirm the contribution of each module in addressing dynamic inter-client spatial dependencies, while sensitivity analysis highlights the robustness of FedSTGD to variations in hyperparameters.

Paper Structure

This paper contains 32 sections, 2 theorems, 23 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Predefined Graph
  4. Publicly Accessible Graphs
  5. Modeling of Inter-Client Spatial Dependency
  6. Preliminaries
  7. Methodology
  8. Federated Formulation of FedSTGD.
  9. 1. Client-Side Data, Embedding, and Spatial Dependency Partitioning.
  10. 2. Client-Side Spatio-Temporal Modeling.
  11. 3. Server-side Model Aggregation.
  12. Federated Nonlinear Computation Decomposition
  13. Graph Node Embedding Augmentation
  14. 1. Non-Linear Mapping.
  15. 2. Softmax Normalization.
  16. ...and 17 more sections

Key Result

Theorem 1

Let $w_{i1}, w_{i2}, \ldots, w_{id}$ be the columns of $\operatorname{MLP}_i(X_i^t) \in \mathbb{R}^{N_i \times d}$ and $v_{i1}, v_{i2}, \ldots, v_{id_N}$ be the columns of $\tilde{E}_{v i} \in \mathbb{R}^{N_i \times d_N}$. Define $\Gamma: \mathbb{R}^{N_i \times d} \times \mathbb{R}^{N_i \times d_N} Then, we have:

Figures (3)

  • Figure 1: Experimental results on the HZMetro dataset. (a) Visualization of dynamic inter-client spatial dependencies; (b) Schematic illustration of intra-client and inter-client spatial dependencies; (c) Performance comparison between FedSTGD and other mainstream methods; (d) Comparison of Federated Nonlinear Computation Decomposition in FedSTGD against AdptPoLU in other mainstream methods; (e) Ablation study on Graph Node Embedding Augmentation module.
  • Figure 2: Overview of the Proposed FedSTGD Framework
  • Figure 3: Parameters Sensitivity Analysis on HZMetro and NYC-Taxi Datasets.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Definition 3
  • Example 1
  • Definition 4
  • Remark 1
  • Theorem 1
  • Theorem 2