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#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.