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-   -   Feature Transform (http://book.caltech.edu/bookforum/showthread.php?t=3986)

Serega 02-11-2013 08:07 PM

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.

yaser 02-11-2013 09:47 PM

Re: Feature Transform
 
Quote:

Originally Posted by Serega (Post 9353)
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.

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).

Serega 02-12-2013 04:51 AM

Re: Feature Transform
 
Thanks for clarification. Yes, I see it now.

diethealthcare 05-23-2017 12:54 PM

Re: Feature Transform
 
:) Great information


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