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Old 02-11-2013, 09:07 PM
Serega Serega is offline
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Join Date: Jan 2013
Location: Virginia, USA
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Default Feature Transform

I don't understand why feature transform formulas have repeated inputs. For example the formula
(3.13) F_2(x) = (1, x_1, x_2, x_2^2, x_1, x_2, x_2^2)
includes untransformed x_1, x_2 twice. Suppose I find some weight vector w and I have
h(x) = sign \left (  [w_0 w_1 w_2 w_3 w_4 w_5 w_6]  dot  [1, x_1, x_2, x_1^2, x_1, x_2, x_2^2]\right )

I can replace it with
h(x) = sign \left (  [w_0 (w_1 + w_2) (w_3+ w_4) w_5  w_6]  dot  [1, x_1, x_2, x_1^2,  x_2^2]\right )
and get the same result. What do we get by including the same variable twice?

Thanks.
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