1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Decision Boundary Line (Linear/Non-Linear)

  1. Nov 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Given a non-linear decision boundary line: (1 + X1)^2 + (2 − X2)^2 = 4

    Argue that while the decision boundary is not linear in terms of X1 and X2, it is linear in terms of X1,X1^2 , X2, and X2^2 .

    3. The attempt at a solution

    I'm honestly not sure. I realize the curve is a circle, but I don't understand how it could be turned linear by having it terms of X1,X1^2 , X2, and X2^2
     
  2. jcsd
  3. Nov 20, 2013 #2
    Is it because we are extending the feature space by including quadratic terms that can address this non-linearity?
     
  4. Nov 20, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It's pretty basic algebra that (1+ X1)^2+ (2- X2)^2= X1^2- 2X1+ 1+ X2^2- 4X2+ 4= 4
    so X1^2- 2X1+ X2^2- 4X2+ 1= 0.

    If you let Y1= X1^2 and Y2= X2^2, then you have Y1- 2X1+ Y2- 4Y1+ 1= 0 which is 'linear in X1, X2, Y1, and Y2".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Decision Boundary Line (Linear/Non-Linear)
Loading...