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Dimensionality Reduction and Volume Minimization: Generalization of the Determinant Minimization Criterion for Reduced Rank Regression Problems
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.ORCID iD: 0000-0002-1542-2690
2005 (English)Report (Other academic)
Abstract [en]

In this article we propose a generalization of the determinant minimization criterion. The problem of minimizing the determinant of a matrix expression has implicit assumptions that the objective matrix is always nonsingular. In case of singular objective matrix the determinant would be zero and the minimization problem would be meaningless. To be able to handle all possible cases we generalize the determinant criterion to rank reduction and volume minimization of the objective matrix. The generalized minimization criterion is used to solve the following ordinary reduced rank regression problem:minrank(X)=kdet(B-XA)(B-XA)T,where A and B are known and X is to be determined. This problem is often encountered in the system identification context.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2005. , 14 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2005:11
Keyword [en]
Volume; Minimization criterion; Determinant; Rank deficient matrix
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-29470OAI: oai:DiVA.org:liu-29470DiVA: diva2:250285
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2013-10-11Bibliographically approved

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Savas, Berkant

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