On Procrustes Contamination in Machine Learning Applications of Geometric Morphometrics

Geometric morphometrics (GMM) is widely used to quantify shape variation, more recently serving as input for machine learning (ML) analyses. Standard practice aligns all specimens via Generalized Procrustes Analysis (GPA) prior to splitting data into training and test sets, potentially introducing statistical dependence and contaminating downstream predictive models. Here, the effects of GPA-induced contamination are formally characterised using controlled 2D and 3D simulations across varying sample sizes, landmark densities, and allometric patterns. A novel realignment procedure is proposed, whereby test specimens are aligned to the training set prior to model fitting, eliminating cross-sample dependency. Simulations reveal a robust "diagonal" in sample-size vs. landmark-space, reflecting the scaling of RMSE under isotropic variation, with slopes analytically derived from the degrees of freedom in Procrustes tangent space. The importance of spatial autocorrelation among landmarks is further demonstrated using linear and convolutional regression models, highlighting performance degradation when landmark relationships are ignored. This work establishes the need for careful preprocessing in ML applications of GMM, provides practical guidelines for realignment, and clarifies fundamental statistical constraints inherent to Procrustes shape space.