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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.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

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