Departmental Papers (ESE)


The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for "learning" piecewise linear scalar functions in two settings: "approximation," where an "oracle" outputs accurate functional values in response to input queries; and "estimation," where only a fixed discrete data base of input-output pairs is available. We provide a local convergence result for the approximation version of the GI algorithm as well as a study of its numerical performance in the estimation setting. We conclude that PLH offers accuracy closed to that of a neural net while requiring, via our GI algorithm, far shorter training time and preserving desired invariant properties unlike any other presently popular basis family.

Document Type

Conference Paper

Subject Area

GRASP, Kodlab

Date of this Version

July 2000


Copyright 2000 IEEE. Reprinted from Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, Volume 3, 2000, pages 259-264.

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NOTE: At the time of publication, author Daniel Koditschek was affiliated with the University of Michigan. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.



Date Posted: 02 June 2008

This document has been peer reviewed.