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

作     者：Powell, Nathan Kurdila, Andrew J. 

作者机构：Virginia Tech Dept Mech Engn Blacksburg VA 24060 USA 

出 版 物：《COMPUTATIONAL MECHANICS》 (计算力学)

年 卷 期：2021年第68卷第2期

页      面：337-356页

核心收录：

学科分类：08[工学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：Theoretical and Applied Mechanics Computational Science and Engineering Classical and Continuum Physics 

摘      要：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-mu(2)(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.