Leaning theory of Cellular Neural Networks based on covariance structural analysis

This paper describes a learning theory of the CNN based on the covariance structure analysis using new numerical integral methods. In general, a Cellular Neural Network (CNN) is defined as a local connected circuit which has continuous state variables x ??Rⁿ. The importance is in that the piece-wise linear function of the CNN has a linear region |x| ?? 1 for x ?? x because the learning method can be constructed only in linear state and measurement equations, and because the linear region can be quantized from the continuous variable x to the multilevel quantized variable f(x) by each 1-bit ???? modulator which is corresponding to a spiking neuron model. That is, our purpose is to determine the weight parameters ?? in the connection matrices A, B, C, D, T and e by the machine learning method for equilibrium points of the CNN states equation x = 0. The covariance structure for the equilibrium point to the linear region will be constructed based on extended Chua´s CNN theorem to have symmetric edges for a_ij = a_ji and asymmetric one-way edge a_ij ?? 0 for a_ji = 0 for A-matrix A = [a_ij].