  Sparsity and missing data problems are very common in spatiotemporal traffic
data collected from various sensing systems. Making accurate imputation is
critical to many applications in intelligent transportation systems. In this
paper, we formulate the missing data imputation problem in spatiotemporal
traffic data in a low-rank tensor completion (LRTC) framework and define a
novel truncated nuclear norm (TNN) on traffic tensors of
location$\times$day$\times$time of day. In particular, we introduce an
universal rate parameter to control the degree of truncation on all tensor
modes in the proposed LRTC-TNN model, and this allows us to better characterize
the hidden patterns in spatiotemporal traffic data. Based on the framework of
the Alternating Direction Method of Multipliers (ADMM), we present an efficient
algorithm to obtain the optimal solution for each variable. We conduct
numerical experiments on four spatiotemporal traffic data sets, and our results
show that the proposed LRTC-TNN model outperforms many state-of-the-art
imputation models with missing rates/patterns. Moreover, the proposed model
also outperforms other baseline models in extreme missing scenarios.
