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This work focuses on radial basis functions containing no parameters with the main objective being to comparatively explore more of their effectiveness. For this, a total of sixteen forms of shapeless radial basis functions are gathered and investigated under the context of the pattern recognition problem through the structure of radial basis function neural networks, with the use of the Representational Capability (RC) algorithm. Different sizes of datasets are disturbed with noise before being imported into the algorithm as ‘training/testing’ datasets. Each shapeless radial basis function is monitored carefully with effectiveness criteria including accuracy, condition number (of the interpolation matrix), CPU time, CPU-storage requirement, underfitting and overfitting aspects, and the number of centres being generated. For the sake of comparison, the well-known Multiquadric-radial basis function is included as a representative of shape-contained radial basis functions. The numerical results have revealed that some forms of shapeless radial basis functions show good potential and are even better than Multiquadric itself indicating strongly that the future use of radial basis function may no longer face the pain of choosing a proper shape when shapeless forms may be equally (or even better) effective.

Numerical Comparison of Shapeless Radial Basis Function Networks in Pattern Recognition