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Cellular neural network with trapezoidal activation function
Author(s) -
Bilgili Erdem,
Göknar İzzet Cem,
Ucan Osman Nuri
Publication year - 2005
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.328
Subject(s) - cellular neural network , activation function , artificial neural network , stability (learning theory) , exponential stability , function (biology) , computer science , separable space , boolean function , matrix (chemical analysis) , mathematics , algorithm , control theory (sociology) , topology (electrical circuits) , nonlinear system , artificial intelligence , mathematical analysis , combinatorics , control (management) , physics , materials science , quantum mechanics , machine learning , evolutionary biology , composite material , biology
This paper presents a cellular neural network (CNN) scheme employing a new non‐linear activation function, called trapezoidal activation function (TAF). The new CNN structure can classify linearly non‐separable data points and realize Boolean operations (including eXclusive OR) by using only a single‐layer CNN. In order to simplify the stability analysis, a feedback matrix W is defined as a function of the feedback template A and 2D equations are converted to 1D equations. The stability conditions of CNN with TAF are investigated and a sufficient condition for the existence of a unique equilibrium and global asymptotic stability is derived. By processing several examples of synthetic images, the analytically derived stability condition is also confirmed. Copyright © 2005 John Wiley & Sons, Ltd.