Eltzner, B, Huckemann, S and Mardia, KV orcid.org/0000-0003-0090-6235 (2018) Torus principal component analysis with applications to RNA structure. Annals of Applied Statistics, 12 (2). pp. 1332-1359. ISSN 1932-6157
Abstract
There are several cutting edge applications needing PCA methods for data on tori, and we propose a novel torus-PCA method that adaptively favors low-dimensional representations while preventing overfitting by a new test—both of which can be generally applied and address shortcomings in two previously proposed PCA methods. Unlike tangent space PCA, our torus-PCA features structure fidelity by honoring the cyclic topology of the data space and, unlike geodesic PCA, produces nonwinding, nondense descriptors. These features are achieved by deforming tori into spheres with self-gluing and then using a variant of the recently developed principal nested spheres analysis. This PCA analysis involves a step of subsphere fitting, and we provide a new test to avoid overfitting. We validate our torus-PCA by application to an RNA benchmark data set. Further, using a larger RNA data set, torus-PCA recovers previously found structure, now globally at the one-dimensional representation, which is not accessible via tangent space PCA.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2018 Institute of Mathematical Statistics. This is an author produced version of a paper accepted for publication in Annals of Applied Statistics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Statistics on manifolds; tori deformation; directional statistics; dimension reduction; dihedral angles; fitting small spheres; principal nested; spheres analysis |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Oct 2017 14:30 |
Last Modified: | 10 Aug 2018 08:58 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/17-AOAS1115 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123042 |