 LFD Book Forum Lecture 14/normalized w

#1
 Andrs Member Join Date: Jul 2012 Posts: 47 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...
#2 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477 Re: Lecture 14/normalized w

Quote:
 Originally Posted by Andrs 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 (which used to be ) is also multiplied by your scale factor , so it remains the same plane.
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