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Andrs 08-22-2012 12:50 PM

Lecture 14/normalized w
 
I have a question about the geometrical interpretation of the requirement that the absolute value of the signal is equal to one ( |wT.xn| = 1).
There may be different parallel hyperplanes that satisfies the basic requirement that the |signal| is > 0. Each plane is defined by an equation were the parameter w is multiplied by a constant (i.e. parallel planes k*w1*x1+k*w2*x2+k*w3*x3 = b in R3). Each plane will have different distances to the point xn. If I require that |signal| is = 1 for xn, I will be chosing one (parallel) hyperplane but it may not be the hyperplane that has the largest distance to xn.
I would appreciate if somebody could elaborate a little more around this condition...

yaser 08-22-2012 02:22 PM

Re: Lecture 14/normalized w
 
Quote:

Originally Posted by Andrs (Post 4287)
I have a question about the geometrical interpretation of the requirement that the absolute value of the signal is equal to one ( |wT.xn| = 1).
There may be different parallel hyperplanes that satisfies the basic requirement that the |signal| is > 0. Each plane is defined by an equation were the parameter w is multiplied by a constant (i.e. parallel planes k*w1*x1+k*w2*x2+k*w3*x3 = b in R3). Each plane will have different distances to the point xn. If I require that |signal| is = 1 for xn, I will be chosing one (parallel) hyperplane but it may not be the hyperplane that has the largest distance to xn.
I would appreciate if somebody could elaborate a little more around this condition...

The offset b (which used to be w_0) is also multiplied by your scale factor k, so it remains the same plane.


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