Mathematical Neural Network (MaNN) Models Part V: Radial basis function (RBF) neural networks (NNs) in Chemometrics, Envirometrics and Medicinometrics (ChEM)

Radial basis function (RBF)-neural network (NN) has a single hidden (radial) layerof neurons with Gaussian kernelas transfer function (TF). The names of many RBF_NNs correspond to the type TF viz. raised cosine-, generalised-binary, q-, Hunt- etc. The product type functions are Lowe, thin-plate and AuPar. The individual neurons in hidden layer of NN operated by TF (RBF, sigmoid) perform non-linear operation and layer as a whole maps input space into higher dimensions.A two phase training involving determination of centers of RBFs by clustering procedures followed by estimation of WRLO (weight vector of connections between neurons of radial and output layers) is the simplest protocol adapted. Although pseudo-inverse and orthogonal procedures are sought after optimization methods in weights refinement, Bayesian Ying-Yang (BYY-), incremental-, reinforced-, rival-penalized-continuous- (RPCL) and life-longlearning are used with success. Universal function approximation theorem, convergence proofs and error boundsimparted a strong theoretical support. The evolution in architecture leads to recurrent-, self-organizing-, growing- and shrinking categories. Clifford/complex-RBF_NNs accept imaginary values for input unlike other RBF category. The trained network is pruned by temporary dynamic decay algorithm. The resource-allocating- (RA-), minimum-RA-, dynamic-decay-adjustment- belong to growing architecture category. The off-spring of RBF_NN are generalized regression- and probabilistic- NNswith statistical flavor. The power of RBF_NN increases with evolution of structure of network and weights of connections. The addition/deletion of RB neurons, connection making/breaking are implementable through mutation operators. Novelty detection, popularized by Grossberg in ART type NNs, is implemented in RBF_NN.Binary hybridization of RBF_NN with wavelets, support vector machines (SVM), self-organizing maps(SOM), logistic regression etc. increased the functional value of this NN. Nature inspired algorithms viz. evolutionary strategy, genetic algorithm, particle swarm optimization(PSO), mimetic approach, honey bee algorithm are instrumental in arriving at viable solution of intractable hard task of simultaneous optimization of number of clusters, their centers/ widths and weights. SOM-Generalised_RBF emulates finite automata.The imbibing capability of RBF_NN, novelty detection, robustcharacter brought it to the forefront in modeling phase of