  Event detection is gaining increasing attention in smart cities research.
Large-scale mobility data serves as an important tool to uncover the dynamics
of urban transportation systems, and more often than not the dataset is
incomplete. In this article, we develop a method to detect extreme events in
large traffic datasets, and to impute missing data during regular conditions.
Specifically, we propose a robust tensor recovery problem to recover low rank
tensors under fiber-sparse corruptions with partial observations, and use it to
identify events, and impute missing data under typical conditions. Our approach
is scalable to large urban areas, taking full advantage of the spatio-temporal
correlations in traffic patterns. We develop an efficient algorithm to solve
the tensor recovery problem based on the alternating direction method of
multipliers (ADMM) framework. Compared with existing $l_1$ norm regularized
tensor decomposition methods, our algorithm can exactly recover the values of
uncorrupted fibers of a low rank tensor and find the positions of corrupted
fibers under mild conditions. Numerical experiments illustrate that our
algorithm can exactly detect outliers even with missing data rates as high as
40%, conditioned on the outlier corruption rate and the Tucker rank of the low
rank tensor. Finally, we apply our method on a real traffic dataset
corresponding to downtown Nashville, TN, USA and successfully detect the events
like severe car crashes, construction lane closures, and other large events
that cause significant traffic disruptions.
