We build a support vector machine classifier for the XOR data set defined by X− =

{(−1, −1), (1, 1)} and X+ = {(−1, 1), (1, −1)}.

(a) Are the classes of the XOR data set linearly separable?

(b) We use the quadratic kernel k(x, y) = (xyT )2 and explicitly map the data to R3, where

we use the squares of the original two-dimensional data as the first two dimensions.

Determine the formula to compute the third dimension.

(c) In the three-dimensional space from (b), determine the normal vector, offset, and

margin of the separation plane that the support vector machine will find.

Solution.pdf

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