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Spatiotemporal traffic data (e.g., link speed/flow) collected from sensornetworks can be organized as multivariate time series with additional spatialattributes. A crucial task in analyzing such data is to identify and detectanomalous observations and events from the data with complex spatial andtemporal dependencies. Robust Principal Component Analysis (RPCA) is a widelyused tool for anomaly detection. However, the traditional RPCA purely relies onthe global low-rank assumption while ignoring the local temporal correlations.In light of this, this study proposes a Hankel-structured tensor version ofRPCA for anomaly detection in spatiotemporal data. We treat the raw data withanomalies as a multivariate time series matrix (location $\times$ time) andassume the denoised matrix has a low-rank structure. Then we transform thelow-rank matrix to a third-order tensor by applying temporal Hankelization. Inthe end, we decompose the corrupted matrix into a low-rank Hankel tensor and asparse matrix. With the Hankelization operation, the model can simultaneouslycapture the global and local spatiotemporal correlations and exhibit morerobust performance. We formulate the problem as an optimization problem and usetensor nuclear norm (TNN) to approximate the tensor rank and $l_1$ norm toapproximate the sparsity. We develop an efficient solution algorithm based onthe Alternating Direction Method of Multipliers (ADMM). Despite having threehyper-parameters, the model is easy to set in practice. We evaluate theproposed method by synthetic data and metro passenger flow time series and theresults demonstrate the accuracy of anomaly detection.

Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection