Difference-based methods for truncating the singular value decomposition

Evans, Dafydd and Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X 2016. Difference-based methods for truncating the singular value decomposition. Communications in Statistics - Simulation and Computation 45 (3) , pp. 863-879. 10.1080/03610918.2013.875572

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Abstract

Given a noisy time series (or signal), one may wish to remove the noise from the observed series. Assuming that the noise-free series lies in some low dimensional subspace of rank r, a common approach is to embed the noisy time series into a Hankel trajectory matrix. The singular value decomposition is then used to deconstruct the Hankel matrix into a sum of rank-one components. We wish to demonstrate that there may be some potential in using difference-based methods of the observed series in order to provide guidance regarding the separation of the noise from the signal, and to estimate the rank of the low dimensional subspace in which the true signal is assumed to lie.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Published online: 23 Jun 2014
Publisher:	Taylor & Francis
ISSN:	0361-0918
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	9 December 2013
Last Modified:	28 Nov 2024 01:30
URI:	https://orca.cardiff.ac.uk/id/eprint/71434

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