Generalization and learning in Volterra and radial basis function networks: a theoretical analysis

The pattern classification and generalization ability of the class of generalized single-layer networks (GSLNs) using techniques from computational learning theory is analyzed. The authors derive necessary and sufficient conditions on the number of training examples required in order to guarantee a particular generalization performance and compare the bounds obtained to those available for (multilayer) feedforward networks of linear threshold elements (LTEs). This allows one to show that, on the basis of currently available bounds, the sufficient number of training examples for GSLNs tends to be considerably less than for feedforward networks of LTEs with the same number of weights. It is also shown that the use of self-structuring techniques for GSLNs may reduce the number of training examples sufficient for good generalization. An explanation for the fact that GSLNs can require a relatively large number of weights is given