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Principal nested shape space analysis of molecular dynamics data

Dryden, Ian L.; Kim, Kwang-Rae; Laughton, Charles A.; Le, Huiling

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Professor of Statistics

Kwang-Rae Kim

Professor of Computational Pharmaceutical Science

Huiling Le


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 sub-space based PCA (Jung et al., 2012). Sub-spaces 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 sub-shape 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.


Dryden, I. L., Kim, K.-R., Laughton, C. A., & Le, H. (2019). Principal nested shape space analysis of molecular dynamics data. Annals of Applied Statistics, 13(4), 2213-2234.

Journal Article Type Article
Acceptance Date Jun 10, 2019
Online Publication Date Nov 28, 2019
Publication Date Nov 28, 2019
Deposit Date Jun 17, 2019
Publicly Available Date Jun 17, 2019
Journal Annals of Applied Statistics
Print ISSN 1932-6157
Electronic ISSN 1941-7330
Publisher Institute of Mathematical Statistics (IMS)
Peer Reviewed Peer Reviewed
Volume 13
Issue 4
Pages 2213-2234
Keywords dimension reduction; manifold; principal components analysis; principal nested spheres; Riemannian; shape
Public URL
Publisher URL
Contract Date Jun 17, 2019


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