How STFAN Revolutionizes Traffic Flow Forecasting with Spatio‑Temporal‑Frequency Attention

Introduction

Intelligent transportation systems depend on accurate traffic flow forecasting. Existing approaches mainly exploit spatio‑temporal correlations in historical data while overlooking inherent frequency characteristics of traffic time series.

This work proposes a frequency‑domain traffic analysis method that integrates attention mechanisms to capture spatial, temporal, and frequency dependencies, resulting in the Spatio‑Temporal‑Frequency Attention Network (STFAN).

Problem Definition

The traffic network is modeled as an undirected graph G = (N, E, A), where N is the set of sensors, E the edges, and A the adjacency matrix. Each sensor records a feature vector X_i^t ∈ ℝ^C at time t. Given M historical observations, the goal is to predict traffic states for the next T steps.

Mathematical formulation of the forecasting task is illustrated in the following equations:

Model Architecture

STFAN consists of stacked spatial modules, spatio‑temporal‑frequency (STF) modules, and a prediction layer. Each STF module contains a spatial attention block and a time‑frequency attention block.

Spatial Attention Module

The spatial attention module combines an embedding layer, a graph convolutional network (GCN), a cross‑attention layer, and a gating mechanism. The embedding layer injects positional information for both graph topology and time steps. The GCN uses Chebyshev polynomial approximation to capture structural dependencies.

Time‑Frequency Attention Module

This module splits traffic features into temporal and frequency domains. The temporal attention block learns hidden relations across time steps using multi‑head self‑attention. The frequency attention block applies discrete Fourier transform (DFT) to extract amplitude and phase components, then uses attention to model hidden correlations in the frequency domain.

Prediction Layer

Two classic 1×1 convolutional layers map the fused spatio‑temporal‑frequency features to multi‑step forecasts. The model is trained with mean absolute error loss.

Experiments

STFAN was evaluated on the PeMS04 and PeMS08 datasets released by the California Department of Transportation. Compared with several baseline models, STFAN achieved significantly lower prediction errors, especially for medium‑ and long‑term horizons. Ablation studies demonstrated that frequency‑domain features contribute substantially to the model’s performance.

Conclusion

STFAN effectively integrates spatial topology, temporal dynamics, and frequency patterns to improve traffic flow prediction. The detailed experimental results, including performance comparison, module ablation, and hyper‑parameter analysis, will be presented in a follow‑up study.