Learning Theory for Estimation of Animal Motion Submanifolds
This paper describes the formulation and experimental testing of a method to estimate 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 approximating 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 introduces linear approximation spaces in $L_\mu ^2\left(S\right)$ that contain approximations of γ corresponding 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.