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For Support Vector Machines, what effect does the degree parameter have on a model, when using a polynomial kernel?

I was able to find an intuitive explanation of the influence of cost and gamma model parameters, but not the effect of the degree parameter when using a polynomial kernel.

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It appears that the degree parameter controls the flexibility of the decision boundary. Higher degree kernels yield a more flexible decision boundary.

Ben-Hur, Asa, and Jason Weston. "A user’s guide to support vector machines." In Data mining techniques for the life sciences, pp. 231. Humana Press, 2010.

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