An Adaptive Cellular Nonlinear Network and its Application

We propose the extension of the classical framework of Cellular Nonlinear Networks (CNN) to incorporate adaptivity of the cells. Adaptivity means that coupling template coefficients can evolve over time according to some specified rule. Here, the rule is described in terms of a differential equation for each template coefficient. It is proposed that this dynamics can be obtained from the gradient flow of an objective function imposed on the network. The extension is exemplified for a signal processing application, namely the principal subspace analysis (PSA). The application illustrates a top-down approach to self-organization from a global objective to local processing and adaptation rules.