Support Vector Machines — Lecture series — Introducing the concept of geometric margin
In the previous post, we spoke about the problem that occurs whenever we try to scale the hyperplane. We also touched on the fact that, if we want to prevent the scale of the hyperplane from causing problems, we can make the hyperplane ‘scale invariant’ by dividing the values of w and b in the equation of the hyperplane by the norm of w.
NOTE: The norm is just a measure of the size or length of a vector
In this short post, we will be talking about the concept of the geometric margin.
Learning objective:
Understand what the geometric margin means.
Main question:
What is the main idea behind the geometric margin?
Consider the image in Fig. 1 below:
In Fig. 1, the term that is used to describe the distance d between the point X and the hyperplane is referred to as the geometric margin.
In the previous post, we spoke about the concept of a functional margin and it may seem as if its meaning is similar to that of the geometric margin, but they are 2 very different ideas.
The functional margin gives information on the level of confidence of our classified prediction, whiles the geometric margin gives information on the distance between the classified point and the hyperplane.
For instance, if we have a functional margin of -50, we are very confident that the classified value is on the left-hand side (negative side) of the hyperplane, because of its large magnitude value.
But if we have a geometric margin of 40, we just know that the distance between a classified point and the hyperplane is a 40 units.
In the next post, we will be looking at how to mathematically derive the equation of the geometric margin.