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Open AccessArticle

A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion

1
School of Science, Dalian Jiaotong University, Dalian 116028, China
2
Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China
3
School of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(5), 531; https://doi.org/10.3390/e21050531
Received: 16 April 2019 / Revised: 9 May 2019 / Accepted: 23 May 2019 / Published: 25 May 2019
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-points. Once a change-point occurs, the distance between the current point and the Riemannian mean of its neighbor points should be a local maximum. A gradient descent algorithm is proposed to calculate the Riemannian mean. Using the Baker–Campbell–Hausdorff formula, the first-order approximation of the Riemannian mean is taken as the initial value of the iterative procedure. The performance of our method was evaluated by numerical examples and manipulator experiments. View Full-Text
Keywords: change-point detection; special Euclidean group; matrix information geometry; Lie algebra change-point detection; special Euclidean group; matrix information geometry; Lie algebra
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Duan, X.; Sun, H.; Zhao, X. A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion. Entropy 2019, 21, 531.

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