Rapid Detection of Hot-spot by Tensor Decomposition with Application to Weekly Gonorrhea Data

TL;DR

This paper introduces a tensor decomposition approach combined with LASSO techniques to detect spatial hot-spots in temporal bio-surveillance data, demonstrated on weekly gonorrhea case data across US states.

Contribution

The paper presents a novel tensor-based method for hot-spot detection that captures structured outliers over space and time, with an integrated statistical detection procedure.

Findings

Effective detection of hot-spots in simulated data.

Successful application to real-world gonorrhea data from US states.

Method outperforms traditional approaches in identifying persistent spatial outliers.

Abstract

In many bio-surveillance and healthcare applications, data sources are measured from many spatial locations repeatedly over time, say, daily/weekly/monthly. In these applications, we are typically interested in detecting hot-spots, which are defined as some structured outliers that are sparse over the spatial domain but persistent over time. In this paper, we propose a tensor decomposition method to detect when and where the hot-spots occur. Our proposed methods represent the observed raw data as a three-dimensional tensor including a circular time dimension for daily/weekly/monthly patterns, and then decompose the tensor into three components: smooth global trend, local hot-spots, and residuals. A combination of LASSO and fused LASSO is used to estimate the model parameters, and a CUSUM procedure is applied to detect when and where the hot-spots might occur. The usefulness of our proposed methodology is validated through numerical simulation and a real-world dataset in the weekly number of gonorrhea cases from $2006$ to $2018$ for $50$ states in the United States.