title: Configuration of continuous piecewise-linear neural networks.
abstract: The problem of constructing a general continuous piecewise-linear neural network is considered in this paper. It is shown that every projection domain of an arbitrary continuous piecewise-linear function can be partitioned into convex polyhedra by using difference functions of its local linear functions. Based on these convex polyhedra, a group of continuous piecewise-linear basis functions are formulated. It is proven that a linear combination of these basis functions plus a constant, which we call a standard continuous piecewise-linear neural network, can represent all continuous piecewise-linear functions. In addition, the proposed standard continuous piecewise-linear neural network is applied to solve some function approximation problems. A number of numerical experiments are presented to illustrate that the standard continuous piecewise-linear neural network can be a promising tool for function approximation.
authors.affiliation: Department of Automation, Tsinghua University, Beijing 100084, P. R. China. swang@mail.tsinghua.edu.cn
authors.forename: Shuning
authors.initials: S
authors.lastname: Wang
authors.forename: Xiaolin
authors.initials: X
authors.lastname: Huang
authors.forename: Khan M
authors.initials: KM
authors.lastname: Junaid
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D017076:Computer-Aided Design; D016014:Linear Models; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated / Q000379:methods*