Capturing Non-linear Neighbourhood Structure: An Autoencoder Approach to Census-based Dimensionality Reduction

Dimensionality reduction underpins geodemographic analysis, yet traditional linear methods like PCA inadequately capture non-linear relationships in spatial socio-economic data. We evaluate the effectiveness of autoencoders as a practical alternative for deriving composite neighbourhood measures from census data. Using 408 variables from the 2021 England and Wales Census across 188,880 Output Areas, we demonstrate autoencoders achieve 19.4% lower reconstruction error than PCA at typical operational dimensions. Improvements are greatest in deprived and demographically complex areas where PCA systematically underperforms. Autoencoders offer parametric projection of new areas, reconstruction-based diagnostics, and reduced parameter sensitivity.