Pattern Classification Using Radial Basis Function Neural Networks Enhanced with the Rvachev Function Method

摘要

The proposed method for classifying clusters of patterns in complex non-convex, disconnected domains using Radial Basis Function Neural Networks (RBFNNs) enhanced with the Rvachev Function Method (RFM) is presented with numerical examples, it-functions are used to construct complex pattern cluster domain, parameters of which are applied to RBFNNs to establish boundaries for classification. The error functional is a convex quadratic one with respect to weight functions which take weight values on the discrete connectors between neurons. Activation function of neurons of RBFNNs is the sgn(-) function and, therefore, the error function is non-smooth. The delta learning rule during training phase is applied. The sub-gradient of the discretized error function is used rather than its gradient, because it is not smooth. The application of the RFM allows for the creation, implementation, and resolution of large heterogeneous NNs capable to solving diverse sets of classification problems with greater accuracy.