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

arXiv: https://arxiv.org/abs/2504.12450 · HTML: https://mlsanity.com/paper/2504.12450/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 59 references that are in the map.
- First posted on arXiv 16 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [FLAML: A Fast and Lightweight AutoML Library](https://mlsanity.com/paper/1911.04706/) (2019)
- [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021)
- [Joint Shapley values: a measure of joint feature importance](https://mlsanity.com/paper/2107.11357/) (2021)
- [Deep trip generation with graph neural networks for bike sharing system expansion](https://mlsanity.com/paper/2303.11977/) (2023)
- [GeoShapley: A Game Theory Approach to Measuring Spatial Effects in Machine Learning Models](https://mlsanity.com/paper/2312.03675/) (2023)
- [A Moran coefficient-based mixed effects approach to investigate spatially varying relationships](https://mlsanity.com/paper/1606.06885/) (2016)
- [Eigenvector spatial filtering for large data sets: fixed and random effects approaches](https://mlsanity.com/paper/1702.06220/) (2017)
- [The importance of scale in spatially varying coefficient modeling](https://mlsanity.com/paper/1709.08764/) (2017)

## Built on by (most cited first, 1 of 1)

- [Do Location Encoders Capture Spatial Effects? A GeoShapley Benchmark Across Scales](https://mlsanity.com/paper/2606.23453/) (2026)

## Abstract (arXiv)

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.