Configuration of continuous piecewise-linear neural networks.
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.
Wang
Shuning
S
Department of Automation, Tsinghua University, Beijing 100084, P. R. China. swang@mail.tsinghua.edu.cn
Huang
Xiaolin
X
Junaid
Khan M
KM
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*