Supervised Learning for Positional Accuracy Improvement of Historical Maps: A Systematic Comparison and Validation

Positional accuracy improvement (PAI) of historical maps involves correcting their inherent geometric distortions, which often limit their usability in modern applications. While supervised learning (SL) methods offer a promising data-driven alternative, systematic comparisons for this task are scarce. This study evaluates six SL algorithms: Linear Models (LM), Generalized Additive Models (GAM), Neural Networks (NNET), Support Vector Machines (SVM), Random Forest (RF), and K-Nearest Neighbors (KNN) for historical map PAI. The evaluation used both a comprehensive simulation study (three distortion types, varied noise/sparsity levels) and two distinct real-world case studies: a preprocessed 1925 urban cadastral map and a 1798 topographic map with large initial misalignments. Performance was assessed using the 2D Root Mean Squared Error within a statistical learning scheme, in which the nonlinear methods significantly outperformed LM for complex distortions. GAM demonstrated consistent robustness across varied conditions, especially with noisy and sparse data, while offering reliable out of sample error estimates and interpretability. In contrast, the other nonlinear methods showed strengths in specific scenarios (e.g., low noise or sufficient data), but no single algorithm proved universally optimal, with performance being highly context dependent. The selection of an SL algorithm for historical map PAI must balance predictive accuracy with robustness, interpretability, generalizability, and extrapolation behavior, considering specific data characteristics and goals. This research provides a comparative framework to guide such choices, aiming to enhance the utility of historical maps.