[Paper Review] Matrix Completion With Variational Graph Autoencoders: Application in Hyperlocal Air Quality Inference

Tien Huu, Duc Minh Nguyen+6 more|arXiv (Cornell University)|Nov 5, 2018

Air Quality Monitoring and Forecasting22 references4 citations

TL;DR

This paper proposes a variational graph autoencoder (AVGAE) for hyperlocal air quality inference using mobile sensor data, modeling spatio-temporal correlations via a street-network-based graph and matrix completion. The method outperforms state-of-the-art kriging and matrix completion models in RMSE and MAE on real-world NO₂ and PM₂.₅ datasets from Antwerp.

ABSTRACT

Inferring air quality from a limited number of observations is an essential task for monitoring and controlling air pollution. Existing inference methods typically use low spatial resolution data collected by fixed monitoring stations and infer the concentration of air pollutants using additional types of data, e.g., meteorological and traffic information. In this work, we focus on street-level air quality inference by utilizing data collected by mobile stations. We formulate air quality inference in this setting as a graph-based matrix completion problem and propose a novel variational model based on graph convolutional autoencoders. Our model captures effectively the spatio-temporal correlation of the measurements and does not depend on the availability of additional information apart from the street-network topology. Experiments on a real air quality dataset, collected with mobile stations, shows that the proposed model outperforms state-of-the-art approaches.

Motivation & Objective

• To address the challenge of inferring hyperlocal air quality from sparse, low-temporal-resolution measurements collected by mobile stations.
• To model spatio-temporal correlations in air pollution data without relying on external data like traffic or weather.
• To formulate air quality inference as a graph-based matrix completion problem using street network topology.
• To develop a deep generative model that captures complex spatial and temporal dependencies in pollution concentration.
• To evaluate the proposed method on real-world mobile sensor data and compare it with state-of-the-art baselines.

Proposed method

• The method models air quality data as a matrix where rows represent street locations and columns represent time slots, with missing entries to be inferred.
• A graph is constructed using the street network of Antwerp, with nodes as locations and edges based on a 200m distance threshold.
• A variational graph autoencoder (AVGAE) is proposed, combining graph convolutional networks (GCNs) in the encoder and decoder with a variational inference framework.
• The model incorporates temporal smoothness via a temporal neighborhood constraint over consecutive time slots.
• The latent space is regularized using a KL divergence term to ensure a prior distribution over latent variables.
• The decoder reconstructs the original matrix using GCN layers without activation functions, while the sigma branch uses sigmoid to ensure positive predictions.

Experimental results

Research questions

• RQ1 Can a graph-based matrix completion approach effectively infer hyperlocal air quality from mobile sensor data?
• RQ2 How does incorporating both spatial and temporal correlations improve inference accuracy compared to traditional methods?
• RQ3 To what extent does a variational graph autoencoder outperform non-graph-based and kriging-based matrix completion models?
• RQ4 Does the model generalize well without requiring external data such as traffic or weather?
• RQ5 How sensitive is the model's performance to hyperparameter choices like the distance threshold or temporal window size?

Key findings

• The AVGAE model achieves the lowest RMSE and MAE across all evaluated methods for both NO₂ and PM₂.₅ pollutants on the real-world dataset.
• For NO₂, AVGAE achieves an RMSE of 14.87 and MAE of 11.03, outperforming the next-best method (RGCNN) by over 10% in both metrics.
• For PM₂.₅, AVGAE achieves an RMSE of 2.01 and MAE of 1.52, significantly outperforming kriging and matrix completion baselines.
• The exponential kriging model performs best among traditional methods, but still underperforms AVGAE, highlighting the advantage of deep graph modeling.
• The ablation study confirms that both the graph structure and the variational autoencoder components are essential for performance, with ablation reducing accuracy by up to 15%.
• The model effectively captures spatio-temporal patterns even with sparse, irregularly sampled mobile data, demonstrating robustness in real-world conditions.