Spatial and temporal regularized compressive sensing for urban traffic monitoring

Abstract

Urban transport system plays an important role in the economic, social, and environmental dimensions of cities. However, transport system is still facing many challenges, such as the traffic congestion issue. With recent advancements in sensor technologies, urban traffic monitoring system is capable of collecting traffic information from new data sources to mitigate these challenges. Traffic information can be used for both real-time traffic management and long term transport planning. Nonetheless, data sparseness is a common issue among these traffic sensor data, which leads to inaccurate or even mistaken results for higher-level traffic data analysis.

To solve the data sparseness issue of traffic sensors, real-world floating car data from Wuhan city is collected and examined in this research. By extracting link-based average traffic speed for road links at different time intervals, an incomplete traffic condition matrix is formulated with missing entries due to the data sparseness issue. The research question can be posed as how to interpolate the missing entries from known sample in the traffic condition matrix. The literature shows that the typical traffic interpolation models are vulnerable to high data loss. On the contrary, compressive sensing based interpolation models in the literature can still perform well under high data loss. However, current compressive sensing based traffic interpolation models are too general owing to their data-driven strategies.

A spatial and temporal regularized compressive sensing model is proposed to fill in the research gap identified from the literature. The model framework is established primarily based on current compressive sensing interpolation models. Using non-negative matrix factorization, the traffic condition matrix can be decomposed into the spatial factor matrix and temporal factor matrix. The model framework further employs the spatial and temporal constraints on the two factor matrices respectively, such as the spatial correlation, network topology, and short-term stability. The proposed model is equivalent to an optimization problem that minimizes errors with the constraints from low rank and spatio-temporal properties. Stochastic gradient descent algorithm is provided to solve the minimization problem of the proposed model.

The proposed model is evaluated using root mean square error with a 5-fold cross validation. The proposed model is competed with temporal KNN model, space-time KNN model, Kriging model, and baseline compressive sensing model under different data loss patterns and data loss ratios (e.g. from 50% to 90%). Results show that the proposed model performs generally better than these models under these scenarios. This research establishes a paradigm for regularized compressive sensing interpolation models. The regularization terms on the spatial factor matrix and temporal factor matrix can be substituted with alternative constraints from domain knowledge. With further extensions, the proposed model has potential to be applied in several future studies such as the traffic data compression and traffic prediction.