A complex-valued neuro-fuzzy inference system and its learning mechanism

In this paper, we present a Complex-valued Neuro-Fuzzy Inference System (CNFIS) and develop its meta-cognitive learning algorithm. CNFIS has four layersan input layer with m rules, a Gaussian layer with K rules, a normalization layer with K rules and an output layer with n rules. The rules in the Gaussian layer map the m-dimensional complex-valued input features to a K-dimensional real-valued space. Hence, we use the Wirtinger calculus to obtain the complexvalued gradients of the real-valued function in deriving the learning algorithm of CNFIS. Next, we also develop the meta-cognitive learning algorithm for CNFIS, referred to as, “Meta-cognitive Complex-valued Neuro-Fuzzy Inference System (MCNFIS)”. CNFIS is the cognitive component of MCNFIS and a selfregulatory learning mechanism that decides what-to-learn, how-to-learn, and when-to-learn in a meta-cognitive framework is its meta-cognitive component. Thus, for every epoch of the learning process, the meta-cognitive component decides if each sample in the training set must be deleted or used to update the parameters of CNFIS or to be reserved for future use. The performances of CNFIS and MCNFIS are studied on a set of approximation and real-valued classification problems, in comparison to existing complexvalued learning algorithms in the literature. First, we evaluate the approximation performances of CNFIS and MCNFIS on a synthetic complex-valued Email addresses: [email protected] (K. Subramanian), [email protected] (S. Suresh) Preprint submitted to Neurocomputing October 25, 2012 Manuscript Click here to view linked References