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I am using an SVM polynomial kernel (statistics toolbox) with order ranging (say) from 3 to 9. When we perform cross validation with rbf function, we intend to determine the sigma and C values. With the best sigma and cost factor value, the trained network is tested on the test set. Do we determine cost function and sigma as well while performing cross-validation using SVM polynomial kernel? The commands that I intend to use are

structtr = svmtrain(z1, trainoutput, 'Kernel_Function', 'Polynomial', 'Polyorder', i,
                    'showplot', false);
grouparousallat = svmclassify(structtr, w1, 'showplot', false);
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With a RBF kernel you use crossvalidation to determine the best {C;sigma} pair (where C is the regularization/cost parameter and sigma is the standard deviation/shape parameter for your kernel).
However, with a polynomial RBF you don't have a sigma since you don't have a Gaussian (or Gaussian-like) kernel (shape).
For the polynomial kernel you might want to determine the best {C;d} pair (where d is the degree of your polynomial).

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  • $\begingroup$ You could perhaps also consider CV over alternative choices of $\kappa$ constant in $(\kappa+x^Tx^\prime)^d$ $\endgroup$
    – Sycorax
    Mar 23 '16 at 20:04

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