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A Question About Kernel Trick

Asked by Karks in Math & Science, Theory, Probability & Statistics

If i have a feature expansion:

{0, 1}^n -> {0, 1}^2n. for example. If n = 3, then

Theta(x1,x2,x3) = (1, x1, x2, x3, x1x2, x1x3, x2x3, x1x2x3): Every possible
"logical OR" from these 3 variables (including 1).

In this case, show K(x,y) for Theta can be computed in polynomial time: poly
(n).

K(x,y) = Theta(x) dot product Theta(y).

In this case, what are Theta(x) and Theta(y), and more specifically, how do i solve this problem?

View the Solution FREE for 30 Days

20091111-EE-VQP-92 - Hierarchy / EE_QW_3_20080625

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