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A Convex Relaxation of a Dimension Reduction Problem Using the Nuclear Norm
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2012 (English)In: Proceedings of the 51st IEEE Conference on Decision and Control, 2012, 2852-2857 p.Conference paper, Published paper (Refereed)
Abstract [en]

The estimation of nonlinear models can be a challenging problem, in particular when the number of available data points is small or when the dimension of the regressor space is high. To meet these challenges, several dimension reduction methods have been proposed in the literature, where a majority of the methods are based on the framework of inverse regression. This allows for the use of standard tools when analyzing the statistical properties of an approach and often enables computationally efficient implementations. The main limitation of the inverse regression approach to dimension reduction is the dependence on a design criterion which restricts the possible distributions of the regressors. This limitation can be avoided by using a forward approach, which will be the topic of this paper. One drawback with the forward approach to dimension reduction is the need to solve nonconvex optimization problems. In this paper, a reformulation of a well established dimension reduction method is presented, which reveals the structure of the optimization problem, and a convex relaxation is derived.

Place, publisher, year, edition, pages
2012. 2852-2857 p.
Keyword [en]
Concave programming, Nonlinear estimation, Regression analysis
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-93281DOI: 10.1109/CDC.2012.6426097ISI: 000327200403035ISBN: 978-1-4673-2064-1 (print)ISBN: 978-1-4673-2065-8 (print)OAI: oai:DiVA.org:liu-93281DiVA: diva2:623916
Conference
51st IEEE Conference on Decision and Control, Maui, Hawaii, USA, 10-13 December, 2012
Available from: 2013-05-29 Created: 2013-05-29 Last updated: 2016-06-22

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Lyzell, ChristianAndersen, MartinEnqvist, Martin

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
  • rtf