So we have a two dimensional predicted space and we want to find the hyper plane which can separate
this space so that each class is in a different part.
Probably you'd have guessed in such a scenario where the data is perfectly separable.
We can draw in finite hyper planes.
Just take any high powered plane and make tiny shifts or tiny rotations and you would get more hyper
planes.
Here you can see three such hyper planes in this figure.
But which of these hyper planes should we choose and why?
One reasonable choices, selecting that hyper plane, which is farthest from the training observations.
That is, we have a hyper plane.
We find the perpendicular distance of all the observations from this hyper plane, the smallest distance
of these observations is called margin in this figure.
You can see that this point is the closest to the iBOT plane.
So the distance of this point from the hyper plane is the margin.
In other words, margin is the farthest minimum distance between observations of the hyper plane.
So whichever hyper plane has maximum value of the margin, that hyper plane will be selected.
And then whatever it is to the left of this plane is classified as blue or class one.
And whatever it is to the right is classified as purple or class to.
This is known as maximal margin classifier.
You can now see what the name stands for.
Because we choose the hyper plane with maximum value of margin.
This is called maximal margin classifier.
Now, I have chosen the hyper plane.
I broady the hyper plane and the two margins on this graph.
And we notice that there are three point which lie on the margin.
If these points were not there, we would have received wider margins.
These points are called support vectors because in a way, these points are supporting these margin
boundaries.
In fact, if you think about it, other points are not important anymore.
Our classifier is completely dependent only on these support vectors.
Any slight movement in any of these support vectors would mean that the classifier will change identification
of such points and classification on the basis of only these few points.
Is a special characteristic of support vector classifier and machines which separate this technique
from any other conventional technique.