  Rapid advances in sensor, wireless communication, cloud computing and data
science have brought unprecedented amount of data to assist transportation
engineers and researchers in making better decisions. However, traffic data in
reality often has corrupted or incomplete values due to detector and
communication malfunctions. Data imputation is thus required to ensure the
effectiveness of downstream data-driven applications. To this end, numerous
tensor-based methods treating the imputation problem as the low-rank tensor
completion (LRTC) have been attempted in previous works. To tackle rank
minimization, which is at the core of the LRTC, most of aforementioned methods
utilize the tensor nuclear norm (NN) as a convex surrogate for the
minimization. However, the over-relaxation issue in NN refrains it from
desirable performance in practice. In this paper, we define an innovative
nonconvex truncated Schatten p-norm for tensors (TSpN) to approximate tensor
rank and impute missing spatiotemporal traffic data under the LRTC framework.
We model traffic data into a third-order tensor structure of (time
intervals,locations (sensors),days) and introduce four complicated missing
patterns, including random missing and three fiber-like missing cases according
to the tensor mode-n fibers. Despite nonconvexity of the objective function in
our model, we derive the global optimal solutions by integrating the
alternating direction method of multipliers (ADMM) with generalized
soft-thresholding (GST). In addition, we design a truncation rate decay
strategy to deal with varying missing rate scenarios. Comprehensive experiments
are finally conducted using real-world spatiotemporal datasets, which
demonstrate that the proposed LRTC-TSpN method performs well under various
missing cases, meanwhile outperforming other SOTA tensor-based imputation
models in almost all scenarios.
