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The Application of an Oblique-Projected Landweber Method to a Model of Supervised Learning
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel.
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2004 (English)Report (Other academic)
Abstract [en]

This report brings together a novel approach to some computer vision problems and a particular algorithmic development of the Landweber iterative algorithm. The algorithm solves a class of high-dimensional, sparse, and constrained least-squares problems, which arise in various computer vision learning tasks, such as object recognition and object pose estimation. The algorithm has recently been applied to these problems, but it has been used rather heuristically. In this report we describe the method and put it on firm mathematical ground. We consider a convexly constrained weighted least-squares problem and propose for its solution a projected Landweber method which employs oblique projections onto the closed convex constraint set. We formulate the problem, present the algorithm and work out its convergence properties, including a rate-of-convergence result. The results are put in perspective of currently available projected Landweber methods. The application to supervised learning is described, and the method is evaluated in a function approximation experiment.

Place, publisher, year, edition, pages
2004. , 36 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2623
Keyword [en]
Projected Landweber, preconditioner, nonnegative constraint, supervised learning, channel representation
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-24052ISRN: LiTH-ISY-R-2623Local ID: 3610OAI: diva2:244368
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2014-08-28Bibliographically approved

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Johansson, BjörnElfving, TommyKozlov, VladimirGranlund, Gösta
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