Integrating Clustering Method in Compactly Supported Radial Basis Function for Surface Approximation

摘要

Radial basis function, one of the mesh-free methods, makes it convenient to interpolate and approximate high dimensional data points. Interpolation fits the data points exactly, whereas approximation fits the data points approximately. The approximation method is more appropriate for large and noisy data points in comparison to the interpolation method. Compactly supported radial basis function is extensively discussed in the literature of approximation theory. It also becomes popular as a result of its computational advantages. Hence, in this study, Wendland's compactly supported radial basis function is chosen. The main contribution of this paper is integrating the clustering procedures to determine the recommended number of reference points, which is expected to provide as few reference points as possible for surface approximation. Three bivariate test functions are selected to generate a moderately large amount of data points followed by the process of adding different levels of noise in order to observe the effectiveness of the proposed method. The results obtained are further confirmed and analysed through error analysis. Finally, the experimental results show that the surfaces are well approximated from the recommended number of reference points gained from the proposed method.