About the Smoothing Filter

You can use the smoothing filter to relax the requirement that the RBF approximation passes through every single data point.

The primary purpose of the smoothing filter is to smooth out noisy data. By not going through every point, Isight can effectively smooth noisy functions and provide an approximation that may be easier to optimize. The value specified by this option averages the output values of points that are clustered in the normalized filter domain.

The filter operates in the Euclidian space with domains normalized to [0,1]. Clustering is performed within that domain. For example, consider an approximation with a single input x, where 0<x<10. For a smoothing filter value of 0.001, Isight clusters and averages all points in the range of 0.719<x<0.721 for the input at x=7.2 (the space x is normalized over the range 10).

The maximum allowed value for the smoothing filter is 0.1. Mathematically, this means you have a maximum of 10 clustered sample points for each input. (Through research, it has been determined that at larger values it does not make sense to perform an RBF.) With 10 clustered sample points, Isight can identify a maximum of four local minima (sine wave) across one dimension. With quartic RSM Isight can identify three local minima across one dimension. Therefore, if you have to use a smoothing filter value greater than 0.1, it is better to use the RSM technique (see Creating a User-Defined Approximation Using the Response Surface Model (RSM) Technique).

There is no theoretical basis to distinguish between signal and noise in the data used for approximation. It is recommended that you evaluate the resultant RBF to determine if this option is appropriate for your application.