Distribution-free learning theory for approximating submanifolds from reptile motion capture data. (English) Zbl 1480.92028
Summary: 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.
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