# Graph Markov Network for Traffic Forecasting with Missing Data

arXiv: https://arxiv.org/abs/1912.05457 · HTML: https://mlsanity.com/paper/1912.05457/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2019.

## Built on by (most cited first, 14 of 14)

- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging](https://mlsanity.com/paper/2109.12144/) (2021)
- [Traffic Prediction using Artificial Intelligence: Review of Recent Advances and Emerging Opportunities](https://mlsanity.com/paper/2305.19591/) (2023)
- [Data-Driven Traffic Assignment: A Novel Approach for Learning Traffic Flow Patterns Using a Graph Convolutional Neural Network](https://mlsanity.com/paper/2202.10508/) (2022)
- [Traffic Forecasting on New Roads Using Spatial Contrastive Pre-Training (SCPT)](https://mlsanity.com/paper/2305.05237/) (2023)
- [Dynamic Spatiotemporal Graph Convolutional Neural Networks for Traffic Data Imputation with Complex Missing Patterns](https://mlsanity.com/paper/2109.08357/) (2021)
- [Because Every Sensor Is Unique, so Is Every Pair: Handling Dynamicity in Traffic Forecasting](https://mlsanity.com/paper/2302.09956/) (2023)
- [Graph Convolutional Networks for Traffic Forecasting with Missing Values](https://mlsanity.com/paper/2212.06419/) (2022)
- [SUSTeR: Sparse Unstructured Spatio Temporal Reconstruction on Traffic Prediction](https://mlsanity.com/paper/2502.16935/) (2025)
- [Transfer learning for cross-modal demand prediction of bike-share and public transit](https://mlsanity.com/paper/2203.09279/) (2022)
- [Explainable Graph Pyramid Autoformer for Long-Term Traffic Forecasting](https://mlsanity.com/paper/2209.13123/) (2022)
- [Fast-PGM: Fast Probabilistic Graphical Model Learning and Inference](https://mlsanity.com/paper/2405.15605/) (2024)
- [PreMixer: MLP-Based Pre-training Enhanced MLP-Mixers for Large-scale Traffic Forecasting](https://mlsanity.com/paper/2412.13607/) (2024)
- [A Map-matching Algorithm with Extraction of Multi-group Information for Low-frequency Data](https://mlsanity.com/paper/2209.08500/) (2022)

## Abstract (arXiv)

Traffic forecasting is a classical task for traffic management and it plays an important role in intelligent transportation systems. However, since traffic data are mostly collected by traffic sensors or probe vehicles, sensor failures and the lack of probe vehicles will inevitably result in missing values in the collected raw data for some specific links in the traffic network. Although missing values can be imputed, existing data imputation methods normally need long-term historical traffic state data. As for short-term traffic forecasting, especially under edge computing and online prediction scenarios, traffic forecasting models with the capability of handling missing values are needed. In this study, we consider the traffic network as a graph and define the transition between network-wide traffic states at consecutive time steps as a graph Markov process. In this way, missing traffic states can be inferred step by step and the spatial-temporal relationships among the roadway links can be Incorporated. Based on the graph Markov process, we propose a new neural network architecture for spatial-temporal data forecasting, i.e. the graph Markov network (GMN). By incorporating the spectral graph convolution operation, we also propose a spectral graph Markov network (SGMN). The proposed models are compared with baseline models and tested on three real-world traffic state datasets with various missing rates. Experimental results show that the proposed GMN and SGMN can achieve superior prediction performance in terms of both accuracy and efficiency. Besides, the proposed models' parameters, weights, and predicted results are comprehensively analyzed and visualized.