Capturing Non‐Linear Neighborhood Structure: An Autoencoder Approach to Census‐Based Dimensionality Reduction for Residential Differentiation

ABSTRACT Dimensionality reduction is fundamental to applied spatial data analysis, condensing high‐dimensional indicators into parsimonious representations for mapping and modeling. Principal component analysis (PCA) remains a dominant approach, yet its linearity assumptions constrain its capacity to capture the complex, non‐linear dependencies characteristic of spatial socio‐economic data. We evaluate the effectiveness of autoencoders as a flexible, parametric alternative for constructing composite measures of neighborhood structure. Through encoder‐decoder architectures, AEs learn non‐linear representations that better reflect underlying data complexity, enable projection of new observations without refitting, and provide reconstruction‐based diagnostics that enhance transparency. We demonstrate the approach using small‐area data from the 2021 Census of England and Wales, evaluating how effectively AEs summarize spatial variability and recover composite dimensions of residential differentiation compared with PCA.