I'm struggling to mathematically determine the equation of the hyperplane and its corresponding geometric margin.
Consider, as example, the following six points, each with two features: 3 points in Class A: (1, 20), (2, 30), (1, 30) and 3 points in Class B: (3, 30), (2, 20), (3, 20)
How would I reason the optimal separating line in this case? I know that the two support vectors are (2, 20) in class B and (2, 30) in class A.
Like you mentioned (2,20) in class B and (2,30) in class A are the support vectors. But (1,20) in class A and (3,30) in class B are also the support vectors. The optimal separating line in this case is one which passes through (1,15) - (2,25) - (3,35) because it ensure that maximum margin is obtained between both the classes.You can try drawing this on paper and observe. If you try drawing some other line which can still perfectly classify, then this line would end up being near points of one class.
