SVM OldKiwi.jpg

We have 3 points. The labels are shown in the figure.


Writing the Equation for the dual problem: SVM1 OldKiwi.jpg


$ Q(\alpha )= {\alpha }_{1}+{\alpha }_{2}+{\alpha }_{3}-[0.5{{\alpha }_{1}}^{2}+0.5{{\alpha }_{2}}^{2}+2{{\alpha }_{3}}^{2}+2{\alpha }_{2}{\alpha }_{3}] $


Subject to constraints

$ -{\alpha }_{1}+{\alpha }_{2}+{\alpha }_{3}=0 $

and $ {\alpha }_{1}\geq 0; {\alpha }_{2}\geq 0;{\alpha }_{3}\geq 0 $ Differentiating partially with respect to $ {\alpha }_{1},{\alpha }_{2}, {\alpha }_{3} $

$ 1-{\alpha }_{1}=0 $

$ 1-{\alpha }_{2}-2{\alpha }_{3}=0 $ $ 1-2{\alpha }_{2}-4{\alpha }_{3}=0 $

We always use the constraint equation, and then use 2 of these three equations. On solving, we get

$ {\alpha }_{1} = 1 $ $ {\alpha }_{2} = 1 $ $ {\alpha }_{3} = 0 $


SVM2 OldKiwi.jpg

b=0

Thus, we get a line through the origin with slope 1. This is the same boundary as was expected.

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett