Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping

D.J. Leith, W.E. Leithead, R. Murray-Smith

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages849-858
Number of pages10
JournalAutomatica
Volume42
Issue number5
DOIs
Publication statusPublished - May 2006

Keywords

  • nonlinear identification
  • dimensionality reduction
  • Gaussian process priors
  • nonlinear mapping

Cite this

Leith, D.J. ; Leithead, W.E. ; Murray-Smith, R. / Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping. In: Automatica. 2006 ; Vol. 42, No. 5. pp. 849-858.
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Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping. / Leith, D.J.; Leithead, W.E.; Murray-Smith, R.

In: Automatica, Vol. 42, No. 5, 05.2006, p. 849-858.

Research output: Contribution to journalArticle

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