Distribution-free learning theory for approximating submanifolds from reptile motion capture data

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, γ , 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 μ 2 ( S ) of approximations of γ 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.