Hyper basis function network
In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the Mahalanobis-like distance is used instead of Euclidean distance measure. Hyper basis function networks were first introduced by Poggio and Girosi in the 1990 paper “Networks for Approximation and Learning”. Network Architecture The typical HyperBF network structure consists of a real input vector , a hidden layer of activation functions and a linear output layer. The output of the network is a scalar function of the input vector, , is given by where is a number of neurons in the hidden layer, and are the center and weight of neuron . The activation function at the HyperBF network takes the following form where is a positive definite matrix. Depending on the application, the following types of matrices are usually considered , where . This case corresponds to the regular RBF network. , where . In this case, the basis functions are radially symmetric, but are scaled with different width. , where . Every neuron has an elliptic shape with a varying size. Positive definite matrix, but not diagonal. Training Training HyperBF networks involves estimation of weights , shape