基于张量分解的热点快速检测方法及其在淋病周数据中的应用
Rapid Detection of Hot-spot by Tensor Decomposition with Application to Weekly Gonorrhea Data
摘要：
在许多生物监测和医疗保健应用中，数据源随着时间的推移从许多空间位置重复测量，例如每天/每周/每月。在这些应用中，我们通常对检测热点感兴趣，热点被定义为在空间域上稀疏但随时间持续的一些结构化离群值。在本文中，我们提出了一种张量分解方法来检测何时何地出现的热点。我们提出的方法将观察到的原始数据表示为三维张量，包括每日/每周/每月模式的圆形时间维度，然后将张量分解为三个分量：平滑的全球趋势，局部热点和残差。LASSO和融合LASSO的组合被用来估计模型参数，和一个CANUUM程序被应用于检测何时何地可能发生的热点。我们所提出的方法的有用性进行了验证，通过数值模拟和真实世界的数据集，在每周的淋病病例数从$2006$到$2018$的$50$国家在美国。
英文摘要：
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.
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