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Abstract:
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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 on a manifold which is far from being flat. Principal nested spheres involves the backwards fitting of a sequence of nested spheres to data, and can lead to striking insights which may be missed using PCA (Jung, Dryden and Marron, 2012, Biometrika). We develop principal nested shape spaces (PNSS) for three-dimensional shape data, and provide some fast fitting algorithms. The methodology is applied to a large set of 100 runs of 3D protein simulations, investigating biochemical function in applications in Pharmaceutical Sciences. The data exhibit distinct clusters, representing different molecular states, and these features are far more apparent using PNSS compared to PCA.
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