Feature Transform

Serega · #1 02-11-2013, 09:07 PM

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

twice. Suppose I find some weight vector

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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