Contents I Introduction
The radial basis function neural network (RBFNN) is a special type of neural network model with several distinctive features [1]–[2]. Since firstly proposed, the RBFNN has attracted a high degree of attention and interest in research communities. And currently it has successfully been exploited in many applications, such as function approximation, pattern classification, and data clustering, etc. One of the main applications for the RBFNN model is pattern recognition or classification [3]–[6]. Usually, when used as a pattern classifier, the outputs of the RBFNN represent the posterior probabilities of the training data by a weighted sum of Gaussian basis functions with diagonal covariance matrices. Generally speaking, the diagonal elements of covariance matrix of input samples are identical, which control the spread of the kernel function (or referred to as transfer function) for the corresponding RBF unit. As a result, the RBF units can perform hyper-spherical division on the input samples. Usually, high recognition accuracy can be achieved when the sample sets are independent. If this case can not be satisfied, more basis functions will be required so that the input data in the region covered by each basis function can still be considered to be independent. In fact, it would be beneficial if the full covariance matrices could be incorporated into the RBFNN structure so that complex distributions could be well represented without the need for using a large number of basis functions. As a result, the RBF units are in hyper-ellipsoidal shapes, and can enhance the approximation capability of conventional RBFNN models. Thus, the elliptical basis function neural networks (EBFNN) can be considered as an extension of the RBFNN for performing pattern classification or function approximation. This paper, therefore, will introduce a novel EBFNN model with the hyper-ellipsoidal units in an attempt to obtain the better classification capability with respect to the conventional RBFNN.
