arXiv:2601.18448cs.CVcs.LG2026-01被引 1

GPA预处理会污染机器学习模型,新方法可消除此问题

On Procrustes Contamination in Machine Learning Applications of Geometric Morphometrics

  • 测试集对齐训练集再建模,避免跨样本依赖
  • 仿真显示误差随样本量和点位数呈特定对角线变化
  • 忽略点间空间相关性会显著降低模型性能

几何形态测量学(GMM)广泛用于量化形状变异,近年被用作机器学习(ML)分析的输入。标准做法是在分割训练与测试集前,通过广义普罗克鲁斯特斯分析(GPA)对所有标本进行对齐,可能引入统计依赖,污染下游预测模型。本文通过2D和3D可控仿真,在不同样本量、点位密度和异速生长模式下,系统刻画了GPA导致的污染效应。提出一种新型重对齐流程:测试样本在建模前先对齐训练集,彻底消除跨样本依赖。仿真结果揭示样本量与点位空间之间存在稳定的“对角线”规律,其斜率可由普罗克鲁斯特斯切空间自由度解析推导。进一步通过线性与卷积回归模型证明点位间空间自相关的重要性,忽略该关系会导致性能下降。本研究确立了在GMM的机器学习应用中需谨慎预处理,提供实用重对齐指南,并阐明普罗克鲁斯特斯形状空间固有的基本统计约束。

原文摘要 · Abstract (English)

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.

几何形态学机器学习形状分析数据预处理

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