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

TL;DR

This paper introduces SSR-Tensor, a fast and robust tensor decomposition method for detecting sparse, temporally consistent hot-spots in spatial-temporal data, demonstrated on crime rate datasets.

Contribution

The paper presents a novel SSR-Tensor approach combining tensor decomposition, LASSO, and CUSUM for rapid hot-spot detection in large-scale spatial-temporal data.

Findings

Achieves fast detection of hot-spots in simulations and real data.

Accurately localizes hot-spots in crime rate analysis.

Outperforms existing methods in speed and accuracy.

Abstract

We propose an efficient statistical method (denoted as SSR-Tensor) to robustly and quickly detect hot-spots that are sparse and temporal-consistent in a spatial-temporal dataset through the tensor decomposition. Our main idea is first to build an SSR model to decompose the tensor data into a Smooth global trend mean, Sparse local hot-spots, and Residuals. Next, tensor decomposition is utilized as follows: bases are introduced to describe within-dimension correlation, and tensor products are used for between-dimension interaction. Then, a combination of LASSO and fused LASSO is used to estimate the model parameters, where an efficient recursive estimation procedure is developed based on the large-scale convex optimization, where we first transform the general LASSO optimization into regular LASSO optimization and apply FISTA to solve it with the fastest convergence rate. Finally, a CUSUM procedure is applied to detect when and where the hot-spot event occurs. We compare the performance of the proposed method in a numerical simulation study and a real-world case study, which contains a dataset including a collection of three 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 detection and accurate localization of the hot-spots.