Open Access
December 2019 Principal nested shape space analysis of molecular dynamics data
Ian L. Dryden, Kwang-Rae Kim, Charles A. Laughton, Huiling Le
Ann. Appl. Stat. 13(4): 2213-2234 (December 2019). DOI: 10.1214/19-AOAS1277


Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA [Biometrika 99 (2012) 551–568]. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D subshape spaces and provide some practical fitting algorithms. The methodology is applied to cluster analysis of peptides, where different states of the molecules can be identified. Also, the temporal transitions between cluster states are explored.


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Ian L. Dryden. Kwang-Rae Kim. Charles A. Laughton. Huiling Le. "Principal nested shape space analysis of molecular dynamics data." Ann. Appl. Stat. 13 (4) 2213 - 2234, December 2019.


Received: 1 September 2018; Revised: 1 March 2019; Published: December 2019
First available in Project Euclid: 28 November 2019

zbMATH: 07160937
MathSciNet: MR4037428
Digital Object Identifier: 10.1214/19-AOAS1277

Keywords: Dimension reduction , Manifold , principal components analysis , principal nested spheres , Riemannian , shape

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 4 • December 2019
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