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Rapid advances in sensor, wireless communication, cloud computing and datascience have brought unprecedented amount of data to assist transportationengineers and researchers in making better decisions. However, traffic data inreality often has corrupted or incomplete values due to detector andcommunication malfunctions. Data imputation is thus required to ensure theeffectiveness of downstream data-driven applications. To this end, numeroustensor-based methods treating the imputation problem as the low-rank tensorcompletion (LRTC) have been attempted in previous works. To tackle rankminimization, which is at the core of the LRTC, most of aforementioned methodsutilize the tensor nuclear norm (NN) as a convex surrogate for theminimization. However, the over-relaxation issue in NN refrains it fromdesirable performance in practice. In this paper, we define an innovativenonconvex truncated Schatten p-norm for tensors (TSpN) to approximate tensorrank and impute missing spatiotemporal traffic data under the LRTC framework.We model traffic data into a third-order tensor structure of (timeintervals,locations (sensors),days) and introduce four complicated missingpatterns, including random missing and three fiber-like missing cases accordingto the tensor mode-n fibers. Despite nonconvexity of the objective function inour model, we derive the global optimal solutions by integrating thealternating direction method of multipliers (ADMM) with generalizedsoft-thresholding (GST). In addition, we design a truncation rate decaystrategy to deal with varying missing rate scenarios. Comprehensive experimentsare finally conducted using real-world spatiotemporal datasets, whichdemonstrate that the proposed LRTC-TSpN method performs well under variousmissing cases, meanwhile outperforming other SOTA tensor-based imputationmodels in almost all scenarios.

Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns