prtKernelRbfNdimensionScale  Auto-scale radial basis function kernel
 
   kernelObj = prtKernelRbfNdimensionScale generates a
   prtKenrelNdimensionScale object implementing a radial basis
   function, but with sigma parameter scaled by the number of features
   in the training data set.  Kernel objects are widely used in several
   prt classifiers, such as prtClassRvm and prtClassSvm.  RBF kernels
   implement the following function for 1 x N vectors x1 and x2:
 
    k(x1,x2) = exp(-sum((x1-x2).^2)./(sigma^2*N));
 
   KERNOBJ = prtKernelRbfNdimensionScale(PROPERTY1, VALUE1, ...) constructs a
   prtKernelRbfNdimensionScale object KERNOBJ with properties as specified by
   PROPERTY/VALUE pairs. prtKernelRbfNdimensionScale objects have the following
   user-settable properties:
 
    sigma   - Positive scalar value specifying the width of the
              Gaussian kernel in the RBF function.  (Default value is 1 )
              This is further scaled by the square root of the number
              of dimensions of the data.
 
   Radial basis function kernels are widely used in the machine
   learning literature. For more information on these kernels, please
   refer to:
    
   http://en.wikipedia.org/wiki/Support_vector_machine#Non-linear_classification
 
    prtKernelRbfNdimensionScale objects inherit the TRAIN, RUN, and AND
    methods from prtKernel.
 
   Radial basis function kernels are widely used in the machine
   learning literature. Auto-scaling these kernels allows for relative
   invariance to the number of dimensions of the data under
   consideration.  For more information on these kernels, please refer
   to:
    
   http://en.wikipedia.org/wiki/Support_vector_machine#Non-linear_classification
 
   % Example:
    ds = prtDataGenBimodal;            % Load a data set
    k1 = prtKernelRbfNdimensionScale;  % Create two
                                       % prtKernelRbfNdimensionScale
                                       % objects
    k2 = prtKernelRbfNdimensionScale('sigma',2);
    
    k1 = k1.train(ds); % Train
    g1 = k1.run(ds);    % Evaluate
 
    k2 = k2.train(ds); % Train
    g2 = k2.run(ds);   % Evaluate
 
    subplot(2,1,1); imagesc(g1.getObservations);  %Plot the results
    subplot(2,1,2); imagesc(g2.getObservations);