Hot-spots Detection in Count Data by Poisson Assisted Smooth Sparse Tensor Decomposition

TL;DR

This paper introduces PoSSTenD, a tensor decomposition method that detects and localizes hot-spots in count data across space, time, and categories, aiding rapid response in bio-surveillance.

Contribution

It develops a novel Poisson-assisted tensor decomposition approach that simultaneously detects hot-spots and localizes their locations in multi-dimensional count data.

Findings

Effective hot-spot detection demonstrated on simulated data.

Successful localization of hot-spots in real-world infectious disease data.

Method outperforms existing techniques in accuracy and interpretability.

Abstract

Count data occur widely in many bio-surveillance and healthcare applications, e.g., the numbers of new patients of different types of infectious diseases from different cities/counties/states repeatedly over time, say, daily/weekly/monthly. For this type of count data, one important task is the quick detection and localization of hot-spots in terms of unusual infectious rates so that we can respond appropriately. In this paper, we develop a method called Poisson assisted Smooth Sparse Tensor Decomposition (PoSSTenD), which not only detects when hot-spots occur but also localizes where hot-spots occur. The main idea of our proposed PoSSTenD method is articulated as follows. First, we represent the observed count data as a three-dimensional tensor including (1) a spatial dimension for location patterns, e.g., different cities/countries/states; (2) a temporal domain for time patterns, e.g., daily/weekly/monthly; (3) a categorical dimension for different types of data sources, e.g., different types of diseases. Second, we fit this tensor into a Poisson regression model, and then we further decompose the infectious rate into two components: smooth global trend and local hot-spots. Third, we detect when hot-spots occur by building a cumulative sum (CUSUM) control chart and localize where hot-spots occur by their LASSO-type sparse estimation. The usefulness of our proposed methodology is validated through numerical simulation studies and a real-world dataset, which records the annual number of 10 different infectious diseases from 1993 to 2018 for 49 mainland states in the United States.