Linguistic rule extraction from a simplified RBF neural network (Q1861617)

A new training algorithm is proposed for the RBF (radial basis function) neural network classifier. The output \(y_m(X)\) of the RBF is described by \(y_m(X)=\sum_{j=1}^Kw_{mj}\varphi_j(X)+w_{m0}b_m\), where \(X\) is the input vector, \(m\) is the number of output class, \(K\) is the number of units in the unique hidden level, \(w_{mj}\) is the weight of \(j\)-th hidden unit in the \(m\)-th output, \(b_m\) is the bias, \(\varphi_j(X)=\exp(-\|X-C_j\|^2/(2\sigma_j^2))\), \(C_j\) and \(\sigma_j\) are the ``center'' and the ``width'' for the \(j\)-th hidden unit. The algorithm selects \(K\), \(C_j\) and \(\sigma_j\) by random search iteratively, \(w_{mj}\) are evaluated by least squares at each step. The stopping rule uses comparison of classification error on the training and validation parts of the sample. The authors describe also a rule extraction from the RBF classifier. Results of classification of Iris and Thyroid data are considered.