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Fuzzy C-means clustering based construction and training for second order RBF network

The paper presents a novel two-step approach for constructing and training of optimally weighted Euclidean distance based Radial-Basis Function (RBF) neural network. Unlike other RBF learning algorithms, the proposed paradigms use Fuzzy C-means for initial clustering and optimal learning factors to train the network parameters (i.e. spread parameter and mean vector). We also introduce an optimized weighted Distance Measure (DM) to calculate the activation function. Newton's algorithm is proposed for obtaining multiple optimal learning factor for the network parameters (including weighted DM). Simulation results show that regardless of the input data dimension, the proposed algorithms are a significant improvement in terms of convergence speed, network size and generalization over conventional RBF models which use a single optimal learning factor. The generalization ability of the proposed algorithm is further substantiated by using k-fold validation.