大数据集的特征向量空间滤波：固定效应和随机效应方法
Eigenvector spatial filtering for large data sets: fixed and random effects approaches
摘要：
特征向量空间滤波（ESF）是一种空间建模方法，已在城市与区域研究、生态学研究等领域得到应用，但其计算量大，不适合大数据量建模。本研究的目的是开发快速ESF和随机效应ESF（RE-ESF），这是能够处理非常大的样本。为了实现这一目标，我们加快了特征分解和参数估计，这使得ESF和RE-ESF变慢。前者是通过利用Nystrom扩展来加速的，而后者是通过小矩阵技巧来加速的。在蒙特卡罗模拟实验中，将得到的快速ESF和快速RE-ESF与非近似ESF和RE-ESF进行了比较。结果表明，ESF和RE-ESF对于几千个样本是慢的，而快速ESF和RE-ESF对于样本仅需要几秒。他们还建议，所提出的方法有效地消除了积极的空间依赖性的残差非常小的近似误差时，考虑的特征向量的数量是200或更多。注意，这些方法不能处理负空间依赖。所提出的方法在R包“spmoran”中实现。"
英文摘要：
Eigenvector spatial filtering (ESF) is a spatial modeling approach, which has been applied in urban and regional studies, ecological studies, and so on. However, it is computationally demanding, and may not be suitable for large data modeling. The objective of this study is developing fast ESF and random effects ESF (RE-ESF), which are capable of handling very large samples. To achieve it, we accelerate eigen-decomposition and parameter estimation, which make ESF and RE-ESF slow. The former is accelerated by utilizing the Nystrom extension, whereas the latter is by small matrix tricks. The resulting fast ESF and fast RE-ESF are compared with non-approximated ESF and RE-ESF in Monte Carlo simulation experiments. The result shows that, while ESF and RE-ESF are slow for several thousand samples, fast ESF and RE-ESF require only several seconds for the samples. They also suggest that the proposed approaches effectively remove positive spatial dependence in the residuals with very small approximation errors when the number of eigenvectors considered is 200 or more. Note that these approaches cannot deal with negative spatial dependence. The proposed approaches are implemented in an R package "spmoran."
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