Configuring the RBF Technique Options

Radial Basis Functions (RBF) are a type of neural network employing a hidden layer of radial units and an output layer of linear units. Elliptical Basis Functions (EBF) are similar to Radial Basis Functions but use elliptical units in place of radial units. Compared to RBF networks where all inputs are handled equally, EBF networks treat each input separately using individual weights.

For more information, see RBF and EBF Models.

  1. Double-click the Approximation component icon .

    The Approximation Component Editor appears.

  2. From the Approximation Component Editor, click the Technique Options tab.

    Enter the Smoothing Filter value. You can use this value to relax the requirement that the RBF approximation passes through every single data point. Its primary purpose 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.

    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.

  3. In the Type of Basis Function list, select Radial or Elliptical.

    RBF networks are characterized by reasonably fast training and reasonably compact networks whereas EBF networks require several iterations to learn individual input weights. EBF networks are often more accurate than RBF networks but can increase initialization time.

  4. If you are using EBF networks, enter the Maximum Iterations to Fit value.

    Isight uses an iterative procedure to learn the weights for individual inputs in the EBF model. Isight limits the maximum number of iterations used to fit a model for each response based on this value.

  5. Click OK to save your changes and to close the Approximation Component Editor.