LFD Book Forum - How to draw the separating line in 2D input

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- - How to draw the separating line in 2D input (http://book.caltech.edu/bookforum/showthread.php?t=4422)

Ahmed.Elkayesh

09-25-2013 09:20 PM

How to draw the separating line in 2D input

This is my first post to the forum and I would like to thank the book authors for the availability online and for choosing to make the book price low.

:clueless:
I have a question and I hope someone will help me answer it

In a 2D input space, we have the components in the W vector, w0 for the bias, and w1, w2 for the 2 dimensions of the input.

If the learning algorithm successfully found the W that could classify all input correctly, how is it possible to draw the separation line(or vector) using the 3 components of the W vector?

How could we map w0,w1,w2 to the Line equation y = ax+ b.

Thanks

Ahmed

yaser

09-27-2013 11:18 PM

Re: How to draw the separating line in 2D input

Quote:

Originally Posted by Ahmed.Elkayesh (Post 11510)

This is my first post to the forum and I would like to thank the book authors for the availability online and for choosing to make the book price low.

:clueless:
I have a question and I hope someone will help me answer it

In a 2D input space, we have the components in the W vector, w0 for the bias, and w1, w2 for the 2 dimensions of the input.

If the learning algorithm successfully found the W that could classify all input correctly, how is it possible to draw the separation line(or vector) using the 3 components of the W vector?

How could we map w0,w1,w2 to the Line equation y = ax+ b.

Thanks

Ahmed

The line would be ${\bf w}^T {\bf x}=0$ which expands as

w_0x_0+w_1x_1+w_2x_2=0

with

x_0=1

and

(x_1,x_2)

being the

(x,y)

coordinates in the conventional

y=ax+b

formulation. As you can see, you need to diivide out by

w_2

to get the coefficient of

x_2

which is

to be 1, hence the discrepancy between the 3 parameters in one formulation and the 2 parameters in the other formulation.

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