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Spatiotemporal Forecasting of Traffic Flow using Wavelet-based Temporal Attention

Yash Jakhmola, Madhurima Panja, Nitish Kumar Mishra, Kripabandhu Ghosh, Uttam Kumar, Tanujit Chakraborty

TL;DR

Spatiotemporal traffic forecasting is challenged by nonstationarity and nonlinear spatial-temporal dependencies. The authors propose W-DSTAGNN, a wavelet-based dynamic spatiotemporal graph neural network that uses MODWT to separate temporal details from trends, then applies wavelet temporal attention and sparse spatial graphs to capture complex patterns. Experiments on PeMS-BAY, PeMS03, and PeMS04 show W-DSTAGNN outperforming ten baselines on 1-hour ahead forecasts and providing reliable conformal prediction intervals, with statistically significant improvements. The approach offers a scalable probabilistic forecasting tool for intelligent transportation systems and can be extended to other spatiotemporal domains.

Abstract

Spatiotemporal forecasting of traffic flow data represents a typical problem in the field of machine learning, impacting urban traffic management systems. In general, spatiotemporal forecasting problems involve complex interactions, nonlinearities, and long-range dependencies due to the interwoven nature of the temporal and spatial dimensions. Due to this, traditional statistical and machine learning methods cannot adequately handle the temporal and spatial dependencies in these complex traffic flow datasets. A prevalent approach in the field combines graph convolutional networks and multi-head attention mechanisms for spatiotemporal processing. This paper proposes a wavelet-based temporal attention model, namely a wavelet-based dynamic spatiotemporal aware graph neural network (W-DSTAGNN), for tackling the traffic forecasting problem. Wavelet decomposition can help by decomposing the signal into components that can be analyzed independently, reducing the impact of non-stationarity and handling long-range dependencies of traffic flow datasets. Benchmark experiments using three popularly used statistical metrics confirm that our proposal efficiently captures spatiotemporal correlations and outperforms ten state-of-the-art models (including both temporal and spatiotemporal benchmarks) on three publicly available traffic datasets. Our proposed ensemble method can better handle dynamic temporal and spatial dependencies and make reliable long-term forecasts. In addition to point forecasts, our proposed model can generate interval forecasts that significantly enhance probabilistic forecasting for traffic datasets.

Spatiotemporal Forecasting of Traffic Flow using Wavelet-based Temporal Attention

TL;DR

Spatiotemporal traffic forecasting is challenged by nonstationarity and nonlinear spatial-temporal dependencies. The authors propose W-DSTAGNN, a wavelet-based dynamic spatiotemporal graph neural network that uses MODWT to separate temporal details from trends, then applies wavelet temporal attention and sparse spatial graphs to capture complex patterns. Experiments on PeMS-BAY, PeMS03, and PeMS04 show W-DSTAGNN outperforming ten baselines on 1-hour ahead forecasts and providing reliable conformal prediction intervals, with statistically significant improvements. The approach offers a scalable probabilistic forecasting tool for intelligent transportation systems and can be extended to other spatiotemporal domains.

Abstract

Spatiotemporal forecasting of traffic flow data represents a typical problem in the field of machine learning, impacting urban traffic management systems. In general, spatiotemporal forecasting problems involve complex interactions, nonlinearities, and long-range dependencies due to the interwoven nature of the temporal and spatial dimensions. Due to this, traditional statistical and machine learning methods cannot adequately handle the temporal and spatial dependencies in these complex traffic flow datasets. A prevalent approach in the field combines graph convolutional networks and multi-head attention mechanisms for spatiotemporal processing. This paper proposes a wavelet-based temporal attention model, namely a wavelet-based dynamic spatiotemporal aware graph neural network (W-DSTAGNN), for tackling the traffic forecasting problem. Wavelet decomposition can help by decomposing the signal into components that can be analyzed independently, reducing the impact of non-stationarity and handling long-range dependencies of traffic flow datasets. Benchmark experiments using three popularly used statistical metrics confirm that our proposal efficiently captures spatiotemporal correlations and outperforms ten state-of-the-art models (including both temporal and spatiotemporal benchmarks) on three publicly available traffic datasets. Our proposed ensemble method can better handle dynamic temporal and spatial dependencies and make reliable long-term forecasts. In addition to point forecasts, our proposed model can generate interval forecasts that significantly enhance probabilistic forecasting for traffic datasets.
Paper Structure (19 sections, 16 equations, 9 figures, 2 tables)

This paper contains 19 sections, 16 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Temporal forecasting approaches
  4. Spatiotemporal forecasting approaches
  5. Wavelet-based forecasters
  6. Mathematical Preliminaries
  7. Wavelet Transformation
  8. Maximal Overlap Discrete Wavelet Transform (MODWT)
  9. Proposed Methodology: W-DSTAGNN
  10. Experimental Setup
  11. Datasets
  12. Baseline models
  13. Performance measure
  14. Experimental setup and performance comparison
  15. Statistical Significance
  16. ...and 4 more sections

Figures (9)

  • Figure 1: Traffic flow data (maroon) alongside its MODWT smooth (purple) and two details (green and orange) coefficients obtained at level 2 decomposition using a Haar wavelet filter. This data represents the traffic flow monitored by the third sensor of (a) PeMS-BAY, (b) PeMS03, and (c) PeMS04 dataset during the first three days of the training period.
  • Figure 2: Detailed framework of the proposed W-DSTAGNN model.
  • Figure 3: Sensor distribution of PeMS-BAY dataset.
  • Figure 4: Heatmap of the correlation values for selected 50 sensor locations of PeMS-BAY dataset.
  • Figure 5: Ground truth data for node 17 of PeMS-BAY on 1st testing day (black) and their corresponding forecasts generated by W-DSTAGNN (red) and DSTAGNN (blue).
  • ...and 4 more figures