Cellular neural network with trapezoidal activation function
MetadataShow full item record
CitationBİLGİLİ, E., GÖKNAR, İ.C., UÇAN, O.N. (2005). Cellular neural network with trapezoidal activation function. International Journal of Circuit Theory and Applications, Volume 33, Issue 5, pp. 393-417.
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.