View Single Post
  #5  
Old 04-20-2013, 04:45 PM
Elroch Elroch is offline
Invited Guest
 
Join Date: Mar 2013
Posts: 143
Default Re: Homework set 3, problem 4 2013

Quote:
Originally Posted by marek View Post
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 w gives a real value w.x to every point x. The points at which w.x=0 form a hyperplane. The points at which w.x>0 are on one side of the hyperplane, the points at which w.x<0 are on the other side. Changing from w to -w, all the values of w.x are multiplied by -1. As a result, the hyperplane where w.x=0 stays the same, but the two regions defined by the sign of w.x swap over.
Reply With Quote