liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Regression on Manifolds with Implications for System Identification
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. (Automatic Control)
2008 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

The trend today is to use many inexpensive sensors instead of a few expensive ones, since the same accuracy can generally be obtained by fusing several dependent measurements. It also follows that the robustness against failing sensors is improved. As a result, the need for high-dimensional regression techniques is increasing.

As measurements are dependent, the regressors will be constrained to some manifold. There is then a representation of the regressors, of the same dimension as the manifold, containing all predictive information. Since the manifold is commonly unknown, this representation has to be estimated using data. For this, manifold learning can be utilized. Having found a representation of the manifold constrained regressors, this low-dimensional representation can be used in an ordinary regression algorithm to find a prediction of the output. This has further been developed in the Weight Determination by Manifold Regularization (WDMR) approach.

In most regression problems, prior information can improve prediction results. This is also true for high-dimensional regression problems. Research to include physical prior knowledge in high-dimensional regression i.e., gray-box high-dimensional regression, has been rather limited, however. We explore the possibilities to include prior knowledge in high-dimensional manifold constrained regression by the means of regularization. The result will be called gray-box WDMR. In gray-box WDMR we have the possibility to restrict ourselves to predictions which are physically plausible. This is done by incorporating dynamical models for how the regressors evolve on the manifold.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2008. , 98 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1382
Keyword [en]
System Identification, High-Dimensional Regression, Manifold, Gray-Box Identification.
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-15467Local ID: LiU-TEK-LIC-2008:40ISBN: 978-91-7393-789-4OAI: diva2:114290
2008-12-04, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (Swedish)
Available from: 2008-11-17 Created: 2008-11-11 Last updated: 2013-10-24Bibliographically approved

Open Access in DiVA

fulltext(1995 kB)884 downloads
File information
File name FULLTEXT01.pdfFile size 1995 kBChecksum SHA-512
Type fulltextMimetype application/pdf
cover(1457 kB)29 downloads
File information
File name COVER01.pdfFile size 1457 kBChecksum SHA-512
Type coverMimetype application/pdf

Search in DiVA

By author/editor
Ohlsson, Henrik
By organisation
Automatic ControlThe Institute of Technology
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 884 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 538 hits
ReferencesLink to record
Permanent link

Direct link