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As far as I understand, the training phase usually uses the dual optimization formulation where we can implicitly calculate the weight vector which defines the discriminant function.

How about the prediction phase, how do we use these weights and the kernel function when a new test sample arrives?

edit: I should clarify, I am interested in the nonlinear SVM.

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For what I understand, once a new document arrives, SVM just applies the discriminant function and decides if the document is going to be classified or not. This would mean that the kernel function is not exploited in the test phase.

You can find a very good introduction to SVM in this tutorial by a UCL PhD student. In addition, this videolecture from the Machine Learning Summer School (from 2006) is very informative as well.

Regards,

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  • $\begingroup$ This is a very good tutorial, thank you. I am interested in the nonlinear case. I suspect that in this case, we never explicitly calculate the weights since we do not know the phi mapping, but we can still evaluate the kernel function using the training samples and the test sample and calculate the discriminant. Yet, it is not crystal clear to me. $\endgroup$ – Zoran May 21 '13 at 7:38
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The transform from a classification to regression of SVM is explained pretty will in this new svm paper. A margin-based loss is used for regression with the loss function max(0, |x - f(x)| - epsilon).

libsvm implemented this idea as well.

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