Spatio-Temporal Constraint-Based Low Rank Matrix Completion Approaches for Road Traffic Networks

Abstract

Road traffic sensing is pivotal in all the imperative services offered by Intelligent Transportation Systems (ITS). Both static and probe based traffic sensing technologies aid in the acquisition of road traffic parameters, represented as spatio-temporal traffic data matrices. These matrices suffer from inevitable data losses, urging accurate matrix reconstruction. Many Low Rank Matrix Completion (LR-MC) approaches have been formulated in the literature, with varied optimization problems and solution methods. The subsequent approaches have exploited spatio-temporal constraints to further reduce the reconstruction error. In this paper, these formulations are modified to develop two new LR-MC approaches, the Augmented Lagrangian Sparsity Regularized Matrix Factorization (AL-SRMF) and the Constrained Low Rank (C-LR). AL-SRMF replaces the Alternating Least Squares (ALS) solution method of SRMF with an AL based method. Optimization in C-LR inherits its temporal constraint from the Temporal and Adaptive Spatial constrained Low Rank (TAS-LR) approach, while adopting its spatial constraint similar to SRMF. Spatial constraint in both C-LR and AL-SRMF is deduced by computing an adjacency matrix that leverages graph notion of the geographical road traffic network. For experimental validations of the proposed approaches, traffic matrices of Californian road network are obtained from PEMS database. Investigations reveal that for a signal integrity (SI) of 0.5, C-LR demonstrated a Normalized Mean Absolute Error (NMAE) of 3.4% and a Root Mean Square Error (RMSE) of 3.2. With a slight increase in computational time, the AL-SRMF rendered least values of NMAE and RMSE, 2.4% and 2.3 respectively, demonstrating significantly better performance than the state-of-the-art approaches.