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1Foundations of Artificial IntelligenceSupport Vector Machines and KernelsCS472 – Fall 2007Thorsten JoachimsOutline•Transform a linear learner into a non-linear learner•Kernels can make high-dimensional spaces tractable•Kernels can make non-vectorial data tractableNon-Linear ProblemsProblem:•some tasks have non-linear structure•no hyperplane is sufficiently accurateHow can SVMs learn non-linear classification rules?ÎExtending the Hypothesis SpaceIdea: add more featuresÎLearn linear rule in feature space.Example:ÎThe separating hyperplane in feature space is degreetwo polynomial in input space.Example•Input Space: (2 attributes)•Feature Space:(6 attributes) Dual (Batch) Perceptron Algorithm
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