14-svm_kernels - Outline Foundations of Artificial...

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1 Foundations of Artificial Intelligence Support Vector Machines and Kernels CS472 – Fall 2007 Thorsten Joachims Outline Transform a linear learner into a non-linear learner Kernels can make high-dimensional spaces tractable Kernels can make non-vectorial data tractable Non-Linear Problems Problem: some tasks have non-linear structure no hyperplane is sufficiently accurate How can SVMs learn non-linear classification rules? Î Extending the Hypothesis Space Idea: add more features Î Learn linear rule in feature space. Example: Î The separating hyperplane in feature space is degree two polynomial in input space. Example Input Space: (2 attributes) Feature Space: (6 attributes) Dual (Batch) Perceptron Algorithm
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