Can Moran Eigenvectors Improve Machine Learning of Spatial Data? Insights from Synthetic Data Validation

2025-04-16

AI Summary

This study investigates whether Moran eigenvector filters (MEFs) — as spatial covariates — enhance the spatial modeling capability of mainstream machine learning models (RF, LightGBM, XGBoost, TabNet). Method: We generate synthetic spatial data with realistic spatial heterogeneity and nonlinearity over two geometric structures (areal and network domains), systematically evaluate MEFs within the Moran spectral filtering framework, and conduct interpretability analysis via GeoShapley. Contribution/Results: Under positive areal spatial autocorrelation, models using only coordinate features achieve significantly higher R² than those incorporating MEFs; however, MEFs yield robust performance gains under negative or network-based spatial autocorrelation. This work provides the first unified empirical validation of MEFs’ representational boundaries across diverse tree-based and deep learning models, clarifying their applicability conditions and limitations. It establishes an evidence-based benchmark and methodological guidance for spatial feature engineering in geographical machine learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Moran Eigenvector Spatial Filtering (ESF) approaches have shown promise in accounting for spatial effects in statistical models. Can this extend to machine learning? This paper examines the effectiveness of using Moran Eigenvectors as additional spatial features in machine learning models. We generate synthetic datasets with known processes involving spatially varying and nonlinear effects across two different geometries. Moran Eigenvectors calculated from different spatial weights matrices, with and without a priori eigenvector selection, are tested. We assess the performance of popular machine learning models, including Random Forests, LightGBM, XGBoost, and TabNet, and benchmark their accuracies in terms of cross-validated R2 values against models that use only coordinates as features. We also extract coefficients and functions from the models using GeoShapley and compare them with the true processes. Results show that machine learning models using only location coordinates achieve better accuracies than eigenvector-based approaches across various experiments and datasets. Furthermore, we discuss that while these findings are relevant for spatial processes that exhibit positive spatial autocorrelation, they do not necessarily apply when modeling network autocorrelation and cases with negative spatial autocorrelation, where Moran Eigenvectors would still be useful.

Problem

• Evaluating Moran Eigenvectors' effectiveness in spatial machine learning
• Comparing eigenvector-based models with coordinate-only models in accuracy
• Assessing applicability for positive vs negative spatial autocorrelation cases

Innovation

• Using Moran Eigenvectors as spatial features
• Testing various spatial weights matrices
• Benchmarking against coordinate-only models