LFD Book Forum Homework set 3, problem 4 2013
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#1
04-20-2013, 04:09 AM
 jjepsuomi Junior Member Join Date: Mar 2013 Posts: 9
Homework set 3, problem 4 2013

Hi,

I'm puzzled with problem 4

Where should I start...should I try to visualize the problem by drawing a picture and simply trying what seems intuitive or what?...

Thank you for any advice
#2
04-20-2013, 11:05 AM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Homework set 3, problem 4 2013

Quote:
 Originally Posted by jjepsuomi Where should I start...should I try to visualize the problem by drawing a picture and simply trying what seems intuitive
That seems like a good approach.
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#3
04-20-2013, 12:39 PM
 jjepsuomi Junior Member Join Date: Mar 2013 Posts: 9
Re: Homework set 3, problem 4 2013

Quote:
 Originally Posted by yaser That seems like a good approach.
Thank you for the help professor
#4
04-20-2013, 04:57 PM
 marek Member Join Date: Apr 2013 Posts: 31
Re: Homework set 3, problem 4 2013

I think I can answer my own question here, but it would add peace of mind to get a confirmation. In the perceptron model, once you fix a dividing line/plane, you still have the choice of which region gets assigned the +1, correct?

I believe this to be the case, because the vector w and the vector -w both give the same geometry, but sign of the two vectors give opposite values. I ask because if this is not the case, and the geometry does fix the region (say "above" the plane is +1), then that would change my answer for #4.
#5
04-20-2013, 05:45 PM
 Elroch Invited Guest Join Date: Mar 2013 Posts: 143
Re: Homework set 3, problem 4 2013

Quote:
 Originally Posted by marek I think I can answer my own question here, but it would add peace of mind to get a confirmation. In the perceptron model, once you fix a dividing line/plane, you still have the choice of which region gets assigned the +1, correct? I believe this to be the case, because the vector w and the vector -w both give the same geometry, but sign of the two vectors give opposite values. I ask because if this is not the case, and the geometry does fix the region (say "above" the plane is +1), then that would change my answer for #4.
A little more completely, a vector gives a real value to every point . The points at which form a hyperplane. The points at which are on one side of the hyperplane, the points at which are on the other side. Changing from to , all the values of are multiplied by . As a result, the hyperplane where stays the same, but the two regions defined by the sign of swap over.
#6
04-20-2013, 05:51 PM
 marek Member Join Date: Apr 2013 Posts: 31
Re: Homework set 3, problem 4 2013

Quote:
 Originally Posted by Elroch A little more completely, a vector gives a real value to every point . The points at which is zero form a hyperplane. The points at which is positive are on one side of the hyperplane, the points at which is negative are on the other side. Changing from to , all the values of are multiplied by . As a result, the hyperplane stays the same, but the two regions defined by the sign of the value of the scalar product swap over.
So then the answer to my question was "yes?"
#7
04-20-2013, 05:55 PM
 Elroch Invited Guest Join Date: Mar 2013 Posts: 143
Re: Homework set 3, problem 4 2013

Yes.

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