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Intelligent transportation systems are a key component in smart cities, and the estimation and prediction of the spatiotemporal traffic state is critical to capture the dynamics of traffic congestion, i.e., its generation, propagation and mitigation, in order to increase operational efficiency and improve livability within smart cities. And while spatiotemporal data related to traffic is becoming common place due to the wide availability of cheap sensors and the rapid deployment of IoT platforms, the data still suffer some challenges related to sparsity, incompleteness, and noise which makes the traffic analytics difficult. In this article, we investigate the problem of missing data or noisy information in the context of real-time monitoring and forecasting of traffic congestion for road networks in a city. The road network is represented as a directed graph in which nodes are junctions (intersections) and edges are road segments. We assume that the city has deployed high-fidelity sensors for speed reading in a subset of edges; and the objective is to infer the speed readings for the remaining edges in the network; and to estimate the missing values in the segments for which sensors have stopped generating data due to technical problems (e.g., battery, network, etc.). We propose a tensor representation for the series of road network snapshots, and develop a regularized factorization method to estimate the missing values, while learning the latent factors of the network. The regularizer, which incorporates spatial properties of the road network, improves the quality of the results. The learned factors, with a graph-based temporal dependency, are then used in an autoregressive algorithm to predict the future state of the road network with a large horizon. Extensive numerical experiments with real traffic data from the cities of Doha (Qatar) and Aarhus (Denmark) demonstrate that the proposed approach is appropriate for imputing the missing data and predicting the traffic state. It is accurate and efficient and can easily be applied to other traffic datasets.

Learning Spatiotemporal Latent Factors of Traffic via Regularized Tensor Factorization: Imputing Missing Values and Forecasting