Piecewise-linear division of region by neural networks with maximum detectors

✍ Scribed by Jian Zhuang; Shun-Ichi Amari

• Book ID: 104591642
• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 477 KB
• Volume: 25
• Category: Article
• ISSN: 0882-1666
• DOI: 10.1002/scj.4690250608

✦ Synopsis

Abstract

A neural network with maximum detectors divides a space which has n‐dimensions R^n^ into piece‐wise‐linear regions. However, there have been very limited theoretical researches concerning what kind of piecewise‐linear region divisions can be realized by a neural network, that is, concerning the formation capability of piecewise‐linear discriminate regions by a neural network.

In this paper, this problem is considered theoretically. The concept of a k‐dividual region is introduced and then it is proved that a division can be realized by a piecewise‐linear machine if and only if it is k‐dividual.