Support vector machine, dimension reduction of hyper plane

Question

Question

I have this question as an assigned task. In 2D the points are {2,4},{1,1},{5,25}{5,25}. I don't know how to officially calculate the optimal separation hyperplane between them, but from the way I did it was to draw a vector from {2,4} to {5,25}, and say that the point half-way between those points is on the hyperplane line. I also say that the line is orthogonal to the vector. This gives the separation line as {3.5,4.5} + t*{-21,3}. I'm not sure of the last step, however; how can I go from a line to a non linear discriminant function?

Answer 1

The discriminant function is just the equation of the line you found (I think). Your line is$x = 3.5 -21t$, $y = 4.5 + 3t$. Now you just eliminate $t$. The second equation gives $3t = y - 4.5$. Plugging this into the first equation, you get $$ x = 3.5 - 7(3t) = 3.5 -7(y - 4.5) $$ And so on.