Supervised models for analyzing three-dimensional shapes

The goal of this paper is to propose supervised learning methods for three-dimensional landmark data. We introduce novel adaptations of Linear Discriminant Analysis (SLDA), Quadratic Discriminant Analysis (SQDA), and K-Nearest Neighbors (Shape-KNN), specifically modified to operate within the non-Euclidean geometry of Kendall’s pre-shape sphere and its corresponding tangent space. To systematically evaluate the performance of the proposed methods, we conducted Monte Carlo simulations, sampling data directly from the manifold using the von Mises-Fisher distribution. The numerical results reveal that SLDA demonstrates superior robustness and stability in high-dimensional, noisy scenarios, whereas SQDA is highly susceptible to the dimensionality when sample sizes are limited. Moreover, we evaluate the models on a real-world 3D dataset. In this application, SQDA achieved the highest accuracy, showcasing its ability to effectively model class-specific covariance structures. Ultimately, this study provides a comprehensive framework and practical guidelines for classifying 3D morphological data in statistical shape analysis.