clf predict (np c_[xx ravel (yy ravel (] reshape (xx shape plt contour (xx yy zcolors =" "plt show (finallywe illustrate the use of the gaussian kernel (xx - kx- ( where is some tuning constant this is an example of radial basis function kernelwhich are reproducing kernels of the form (xx (kx )for some positive realvalued function each feature vector is now transformed to function ( *we can think of it as the (unnormalizedpdf of gaussian distribution centered around xand gt is (signedmixture of these pdfsplus constantthat isgt (xa ai - kxi -xk = replacing in line of the previous code mykernel with 'rbfproduces the svm parameters given in table figure shows the decision boundarywhich is not exactly circularbut is close to the true (circularboundary { kxk / there are now seven support vectorsrather than the four in figure table optimal support vector machine parameters for the gaussian kernel case xy ( xy ( - - - - - - - - - - - - - - - - - - - - figure leftthe decision boundary { gt ( is roughly circularand separates the two classes well there are seven support vectorsindicated by green circles rightthe graph of gt is scaled mixture of gaussian pdfs plus constant