  Spatiotemporal traffic time series (e.g., traffic volume/speed) collected
from sensing systems are often incomplete with considerable corruption and
large amounts of missing values, preventing users from harnessing the full
power of the data. Missing data imputation has been a long-standing research
topic and critical application for real-world intelligent transportation
systems. A widely applied imputation method is low-rank matrix/tensor
completion; however, the low-rank assumption only preserves the global
structure while ignores the strong local consistency in spatiotemporal data. In
this paper, we propose a low-rank autoregressive tensor completion (LATC)
framework by introducing \textit{temporal variation} as a new regularization
term into the completion of a third-order (sensor $\times$ time of day $\times$
day) tensor. The third-order tensor structure allows us to better capture the
global consistency of traffic data, such as the inherent seasonality and
day-to-day similarity. To achieve local consistency, we design the temporal
variation by imposing an AR($p$) model for each time series with coefficients
as learnable parameters. Different from previous spatial and temporal
regularization schemes, the minimization of temporal variation can better
characterize temporal generative mechanisms beyond local smoothness, allowing
us to deal with more challenging scenarios such "blackout" missing. To solve
the optimization problem in LATC, we introduce an alternating minimization
scheme that estimates the low-rank tensor and autoregressive coefficients
iteratively. We conduct extensive numerical experiments on several real-world
traffic data sets, and our results demonstrate the effectiveness of LATC in
diverse missing scenarios.
