Maximum margin hyperplane

From our knowledge of linear algebra, we know that the equation of a plane is given by the following:

In SVM, this plane should separate the positive classes (y= 1) from the negative classes (y=-1), and there's an additional constrain: the distance (margin) of this hyperplane from the closest positive and negative training vectors (Xpos and Xneg respectively) should be maximum. Hence, the plane is called the maximum margin separator.

The vectors Xpos and Xneg are called support vectors, and they play an important role in defining the SVM model.

Mathematically, this means that the following is true:

And, so is this: ...

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