Eigenvector spatial filtering for large data sets: fixed and random effects approaches

TL;DR

This paper introduces fast eigenvector spatial filtering methods, ESF and RE-ESF, optimized for large datasets by accelerating eigen-decomposition and estimation, enabling rapid spatial modeling with minimal approximation errors.

Contribution

It develops computationally efficient versions of ESF and RE-ESF for large data, using Nystrom extension and matrix tricks, and implements them in an R package.

Findings

Fast ESF and RE-ESF require only seconds for large samples.

They effectively remove positive spatial dependence with minimal approximation errors.

Approaches cannot handle negative spatial dependence.

Abstract

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."