ROBUST TEMPLATE DECOMPOSITION WITH RESTRICTED WEIGHTS FOR CELLULAR NEURAL NETWORKS IMPLEMENTING AN ARBITRARY BOOLEAN FUNCTION
Abstract
In this paper, a general problem of the robust template decomposition with restricted weights for cellular neural networks (CNNs) implementing an arbitrary Boolean function is investigated. First, the geometric margin of a linear classifier with respect to a training data set is used to define the robustness of an uncoupled CNN implementing a linearly separable Boolean function. Second, maximal margin classifiers, i.e. robust CNNs, for such Boolean functions can be designed via support vector machines (SVMs). Third, some general properties of robust CNNs with or without restricted weights are discussed. Moreover, all robust CNNs with restricted weights are characterized. Finally, for an arbitrarily given Boolean function, we propose an algorithm, which is the generalized version of the well-known CFC algorithm, to find a sequence of robust uncoupled CNNs implementing the given Boolean function. Several illustrative examples demonstrate the efficiency of the proposed method. It will be seen that, in general, the tradeoff between the complexity regarding the number of terms in the decomposition and the guaranteed robustness regarding the geometric margins of the resulting CNNs must be made in the robust template decomposition with restricted weights.
