  Traffic data chronically suffer from missing and corruption, leading to
accuracy and utility reduction in subsequent Intelligent Transportation System
(ITS) applications. Noticing the inherent low-rank property of traffic data,
numerous studies formulated missing traffic data recovery as a low-rank tensor
completion (LRTC) problem. Due to the non-convexity and discreteness of the
rank minimization in LRTC, existing methods either replaced rank with convex
surrogates that are quite far away from the rank function or approximated rank
with nonconvex surrogates involving many parameters. In this study, we proposed
a Parameter-Free Non-Convex Tensor Completion model (TC-PFNC) for traffic data
recovery, in which a log-based relaxation term was designed to approximate
tensor algebraic rank. Moreover, previous studies usually assumed the
observations are reliable without any outliers. Therefore, we extended the
TC-PFNC to a robust version (RTC-PFNC) by modeling potential traffic data
outliers, which can recover the missing value from partial and corrupted
observations and remove the anomalies in observations. The numerical solutions
of TC-PFNC and RTC-PFNC were elaborated based on the alternating direction
multiplier method (ADMM). The extensive experimental results conducted on four
real-world traffic data sets demonstrated that the proposed methods outperform
other state-of-the-art methods in both missing and corrupted data recovery. The
code used in this paper is available at:
https://github.com/YoungHe49/T-ITSPFNC.
