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Old 02-11-2013, 10:47 PM
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yaser yaser is offline
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,478
Default Re: Feature Transform

Originally Posted by Serega View Post
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?

The last appearance of x_1 and x_2 in the transform formula is actually x_1 x_2 (multiplied) not x_1,x_2 (with a comma).
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