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The Application of an Oblique-Projected Landweber Method to a Model of Supervised Learning

Bjorn Johansson (bjorn***at***isy.liu.se)
Tommy Elfving (toelf***at***mai.liu.se)
Vladimir Kozlov (vlkoz***at***mai.liu.se)
Yair Censor (yair***at***math.haifa.ac.il)
Per-Erik Forssen (perfo***at***isy.liu.se)
Gosta Granlund (gosta***at***isy.liu.se)

Abstract: This paper brings together a novel information representation model for use in signal processing and computer vision problems, with a particular algorithmic development of the Landweber iterative algorithm. The information representation model allows a representation of multiple values for a variable as well as expression of confidence. Both properties are important for effective computation using multi-level models, where a choice between models shall be implementable as part of the optimization process. It is shown that in this way the algorithm can deal with 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. While the algorithm has been applied to the solution of such problems, it has so far been used heuristically. In this paper we describe the properties and some of the peculiarities of the channel representation and optimization, and put them on firm mathematical ground. We consider for the optimization 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. An application to supervised learning is described, and the method is evaluated in an experiment involving function approximation, as well as application to transient signals.

Keywords: Projected Landweber, preconditioner, nonnegative constraint, supervised learning, channel representation

Category 1: Applications -- Science and Engineering

Category 2: Applications -- Science and Engineering (Other )

Citation: Mathematical and Computer Modelling, Vol. 43 (2006), pp. 892-909.

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Entry Submitted: 12/15/2005
Entry Accepted: 12/15/2005
Entry Last Modified: 04/30/2006

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