Leith, Douglas J. and Leithead, W.E. and Murray-Smith, R. (2006) Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping. Automatica, 42 (5). pp. 849-858. ISSN 0005-1098

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Abstract

This paper investigates new ways of inferring nonlinear dependence from measured data. The existence of unique linear and nonlinear sub-spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub-spaces are derived. The importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task. Specifically, once the linear/nonlinear sub-spaces are known, by definition the explanatory variables may be transformed to form two disjoint sub-sets spanning, respectively, the linear and nonlinear sub-spaces. The nonlinear modelling task is confined to the latter sub-set, which will typically have a smaller number of elements than the original set of explanatory variables. Constructive algorithms are proposed for inferring the linear and nonlinear sub-spaces from noisy data.

Item Type:	Article
Additional Information:	The original publication is available at http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V21-4JJ84DF-2-KD&_cdi=5689&_user=107385&_orig=browse&_coverDate=05%2F31%2F2006&_sk=999579994&view=c&wchp=dGLzVtb-zSkzV&md5=6351f86cf7f2ac3982fe54fcfa34fe3f&ie=/sdarticle.pdf
Keywords:	Nonlinear identification; Dimensionality reduction; Gaussian process priors; Hamilton Institute.
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	1792
Identification Number:	https://doi.org/10.1016/j.automatica.2006.01.019
Depositing User:	Hamilton Editor
Date Deposited:	18 Jan 2010 16:35
Journal or Publication Title:	Automatica
Publisher:	Elsevier
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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