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Max 2/||w|| s.t. y(x*w+b)-1 >=0
If data is not linearly separable, a kernel function can be used to map data into a space where it is linearly separable.
Input Space →Kernel Function →Feature Space →Input Space.
Quadratic programming provides a decision function:
D(x) = ∑ ∝ k(xi,xj) + b such that if D(x) >0 then x ∊ A
Kernel Functions
Mapping function x→φ(x)
linear kernel
k(xi,xj)=xi'xj
radial basis kernel
k(xi,xj) = exp[-(||xi –xj||2 / 2 σ2 )]
polynomial kernel
k(xi,xj) = (xixj + a)b
sigmoidal kernel
k(xi ,xj) = tanh(xixj - b)
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