This paper describes the formulation and experimental testing of an estimation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold, Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by finding an unknown mapping, \(\gamma \), from S to Q. The overall problem is cast as a distribution-free learning problem over the manifold of measurements. This paper defines sufficient conditions that show that the rates of convergence in \(L^2_\mu (S)\) of approximations of \(\gamma \) correspond to those known for classical distribution-free learning theory over Euclidean space. This paper concludes with a study and discussion of the performance of the proposed method using samples from recent reptile motion studies.

本文描述了动物运动子流形模型估计的公式化和实验测试。假设动物运动由一个配置流形Q 支持，并且该流形同胚于一个已知的光滑黎曼流形S。配置子流形的估计是通过找到从S到Q的未知映射\(\gamma \)来实现的。整个问题被视为在测量流形上的无分布学习问题。本文定义了充分条件，表明\(\gamma \)的近似值\(L^2_\mu (S)\)的收敛速度对应于欧几里德空间上的经典无分布学习理论。本文最后使用来自最近爬行动物运动研究的样本对所提出方法的性能进行了研究和讨论。