Upper bounds on RBFN designed by input clustering

In the design of radial basis function networks (RBFNs), several heuristic hybrid learning methods, including a clustering algorithm for locating the centers and a linear least-squares method for the linear weights, have been previously suggested. These hybrid methods can be put into two groups depending on whether the output vector is also involved in the clustering process, which is called the input clustering (IC) and input-output clustering (IOC). A recent paper by Uykan et al. (1998) presents a clustering-based upper bound on the RBFN output error designed by IOC. The main contribution of this paper is to obtain a similar upper bound for the IC case which explicitly depends on the RBFN parameters. This paper also presents some different upper bounds for l ₁ and l₂ norms used for the quantisation error and the output error in both IC and IOC cases