Reviewing and designing pre-processing units for RBF networks: initial structure identification and coarse-tuning of free parameters

This paper reviews some frequently used methods to initialize an radial basis function (RBF) network and presents systematic design procedures for pre-processing unit(s) to initialize RBF network from available input–output data sets. The pre-processing units are computationally hybrid two-step training algorithms that can be named as (1) construction of initial structure and (2) coarse-tuning of free parameters. The first step, the number, and the locations of the initial centers of RBF network can be determined. Thus, an orthogonal least squares algorithm and a modified counter propagation network can be employed for this purpose. In the second step, a coarse-tuning of free parameters is achieved by using clustering procedures. Thus, the Gustafson–Kessel and the fuzzy C-means clustering methods are evaluated for the coarse-tuning. The first two-step behaves like a pre-processing unit for the last stage (or fine-tuning stage—a gradient descent algorithm). The initialization ability of the proposed four pre-processing units (modular combination of the existing methods) is compared with three non-linear benchmarks in terms of root mean square errors. Finally, the proposed hybrid pre-processing units may initialize a fairly accurate, IF–THEN-wise readable initial model automatically and efficiently with a minimum user inference.