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**Unformatted text preview: **2 || || 2 Margin w = -≤ + •-≥ + • = 1 b x w if 1 1 b x w if 1 ) ( i i i x f 2 || || ) ( 2 w w L = Support Vector Machines • What if the problem is not linearly separable? Support Vector Machines • What if the problem is not linearly separable? – Introduce slack variables • Need to minimize: • Subject to: +-≤ + •-≥ + • = i i i i 1 b x w if 1-1 b x w if 1 ) ( ξ i x f + = ∑ = N i k i C w w L 1 2 2 || || ) ( Nonlinear Support Vector Machines • What if decision boundary is not linear? Nonlinear Support Vector Machines • Transform data into higher dimensional space...

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