HRST-LR: A Hessian Regularization Spatio-Temporal Low Rank Algorithm for Traffic Data Imputation

Intelligent Transportation Systems (ITSs) are vital for alleviating traffic congestion and improving traffic efficiency. Due to the delay of network transmission and failure of detectors, massive missing traffic data are often produced in ITSs, which evidently decreases the accuracy of decision-making in road traffic management. Hence, how establishing a precise and efficient estimation of missing traffic data becomes a hot yet thorny issue. Low-rank matrix completion (LR-MC) model has proven to be highly effective to address this issue owing to its fine representativeness of such high-dimensional and incomplete data. However, the existing LR-MC models mostly fail to model the inherently temporal and spatial correlations hidden in traffic network structure, resulting in low estimation accuracy. To improve it, this paper proposes a Hessian regularization spatio-temporal low rank (HRST-LR) algorithm with three main-fold ideas: a) imposing low-rank property into the global features of a traffic matrix for precisely learning its structure, b) capturing the temporal evolvement via a second-order difference of time-series constraint, and c) modeling the similar space of road segments through a Hessian regularization spatial constraint, thus exploring the local correlation between road segments for representing the spatial patterns in the traffic data. Experimental results on four traffic data sets prove that HRST-LR outperforms several state-of-the-art methods in the missing traffic data estimation with the root mean squared error improvements often higher than 14% when the missing rate is 90%. Hence, the HRST-LR algorithm is highly valuable for traffic data imputation with the need of performing spatio-temporal low-rank analysis.