The application of an oblique-projected Landweber method to a model of supervised learning |
| |
Institution: | 1. Computer Vision Laboratory, Department of Electrical Engineering, Linköping University, SE-581 83, Linköping, Sweden;2. Scientific Computing Division, Department of Mathematics, Linköping University, SE-581 83, Linköping, Sweden;3. Applied Mathematics Division, Department of Mathematics, Linköping University, SE-581 83, Linköping, Sweden;4. Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel |
| |
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 an expression for confidence. Both properties are important for effective computation using multi-level models, where a choice between models will 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 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 with 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: | |
本文献已被 ScienceDirect 等数据库收录! |
|