Traffic data exhibit the spatiotemporal heterogeneity. Revealing traffic system correlations (TSC) from traffic data, which refers to discovering inter-station correlations incurred from movements of passengers, is a meaningful task for releasing traffic congestion and sustainable urban operations. Since traffic data involve a great loss or corruption due to equipment and transmission failures, traffic data completion (TDC) serves as a necessary task for TSC exploration. We observe that: for the TDC task, traffic data exhibit anisotropic periodicity and repetition along different temporal dimensions, which cannot be captured by traditional low-rank TDC methods; for the TSC exploration task, a traffic network obeys graphical structure and exhibits a strong spatial correlation between stations or road segments. Based on these observations, we propose a Tensorial Weighted Schatten-pNorm model with Neighbor Regularization (TWSN2R) for accomplishing the two tasks simultaneously. TWSN2R consists of a tensorial weighted Schatten-p norm term and a neighbor regularization term. The first term mines the anisotropic periodicity with a tensor form of weighted Schatten-p norm which preserves suitable rank components of traffic data by allocating different weights in both tensorial dimension and decomposed mode dimension. The second term mines a spatial correlation of a traffic network by enforcing a neighbor contribution of passenger flows incurred from the network, and extrinsically reveals an inter-station (or inter-road-segment) TSC of the network. Experiments on the subway flow dataset MetroBJ and the road network vehicle speed dataset RoadBJ demonstrate that, TWSN2R not only outperforms several state-of-the-art TDC methods, but also reveals two pieces of regulations of TSC. (a) For subway passenger flows, positive correlated stations and negative correlated stations contribute to passenger flows differently according to each station’s attributes. (b) For road networks, urban loops, expressways and transportation hubs contribute to the vehicle flows at a majority, and serve as the critical roads for mitigating the congestion of whole road networks.
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