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We propose an efficient statistical method (denoted as SSR-Tensor) torobustly and quickly detect hot-spots that are sparse and temporal-consistentin a spatial-temporal dataset through the tensor decomposition. Our main ideais first to build an SSR model to decompose the tensor data into a Smoothglobal trend mean, Sparse local hot-spots, and Residuals. Next, tensordecomposition is utilized as follows: bases are introduced to describewithin-dimension correlation, and tensor products are used forbetween-dimension interaction. Then, a combination of LASSO and fused LASSO isused to estimate the model parameters, where an efficient recursive estimationprocedure is developed based on the large-scale convex optimization, where wefirst transform the general LASSO optimization into regular LASSO optimizationand apply FISTA to solve it with the fastest convergence rate. Finally, a CUSUMprocedure is applied to detect when and where the hot-spot event occurs. Wecompare the performance of the proposed method in a numerical simulation studyand a real-world case study, which contains a dataset including a collection ofthree types of crime rates for U.S. mainland states during the year 1965-2014.In both cases, the proposed SSR-Tensor is able to achieve the fast detectionand accurate localization of the hot-spots.

Rapid Detection of Hot-spots via Tensor Decomposition with applications to Crime Rate Data