Rapid detection of hot-spots via tensor decomposition with applications to crime rate data
Rapid detection of hot-spots via tensor decomposition with applications to crime rate data
复制标题
通过张量分解快速检测热点并应用于犯罪率数据
DOI：
10.1080/02664763.2021.1874892
复制
发表时间：
2020-04
影响因子：
1.5
通讯作者：
Yujie Zhao;Hao Yan;S. Holte;Y. Mei
中科院分区：
文献类型：
--
作者：
Yujie Zhao;Hao Yan;S. Holte;Y. Mei
摘要在许多监测随时间非平稳的多变量时空数据的实际应用中，人们通常对检测具有空间稀疏性和时间一致性的热点感兴趣，而不是像传统统计过程控制（SPC）文献中那样检测系统变化。在本文中，我们提出了一种有效的方法来检测热点，通过张量分解，我们的方法有三个步骤。首先，我们将观察到的数据拟合到平滑稀疏分解张量（SSD-Tensor）模型中，该模型用作降维和去噪技术：它是一种将原始数据分解为平滑但非平稳的全局均值、稀疏局部异常和随机噪声的加性模型。其次，我们估计模型参数的惩罚框架，其中包括最小绝对收缩和选择算子（LASSO）和融合LASSO惩罚。在快速迭代收缩保持算法（FISTA）的基础上，提出了一种高效的递归优化算法。最后，我们应用累积和控制图（Cumulative Sum Control Chart）来监控去除全局均值后的模型残差，这有助于检测热点何时何地出现。为了证明我们提出的SSD张量方法的有用性，我们比较了它与其他几种方法，包括扫描统计，LASSO为基础的，PCA为基础的，T2为基础的控制图在广泛的数值模拟研究和真实的犯罪率数据集。
ABSTRACT In many real-world applications of monitoring multivariate spatio-temporal data that are non-stationary over time, one is often interested in detecting hot-spots with spatial sparsity and temporal consistency, instead of detecting system-wise changes as in traditional statistical process control (SPC) literature. In this paper, we propose an efficient method to detect hot-spots through tensor decomposition, and our method has three steps. First, we fit the observed data into a Smooth Sparse Decomposition Tensor (SSD-Tensor) model that serves as a dimension reduction and de-noising technique: it is an additive model decomposing the original data into: smooth but non-stationary global mean, sparse local anomalies, and random noises. Next, we estimate model parameters by the penalized framework that includes Least Absolute Shrinkage and Selection Operator (LASSO) and fused LASSO penalty. An efficient recursive optimization algorithm is developed based on Fast Iterative Shrinkage Thresholding Algorithm (FISTA). Finally, we apply a Cumulative Sum (CUSUM) Control Chart to monitor model residuals after removing global means, which helps to detect when and where hot-spots occur. To demonstrate the usefulness of our proposed SSD-Tensor method, we compare it with several other methods including scan statistics, LASSO-based, PCA-based, T2-based control chart in extensive numerical simulation studies and a real crime rate dataset.