When we start our discussion on maximal marginal classifier, the first thing we need to understand
is the concept of a hybrid plain.
Simply put, a hyper plane is something that divides up be dimensional space in two parts.
Don't be carried away by the word plane in its name.
It is not always a two dimensional plane.
It depends on how many dimensions we are considering.
Let's consider a one dimensional space or it's a one dimensional space.
It's a line.
And how do we separate this line into two parts?
We just need a point.
Now, there's a left part of the line which is left to this point and there is a right part of the line.
This point is a hyperbole for this piece.
If we take a two dimensional space, we can separate it using a line you can see here in this diagram.
We have a two dimensional space, which is a plane.
And we can separated using a lane and there will be a path to the left and a path to the right of this
lane.
So for our two dimensional space, we have a one dimensional separator.
That is a line.
Similarly, if I continue increasing the dimensions of space, let's say a three dimensional space.
It can be separated using our two dimensional plane.
So this concept can be extended to any p dimensional space.
And we will see that there is a hybrid plane of B minus one dimensions, which separates this B dimensional
space into two parts.
But you may be thinking, why are we talking about, B, dimensional spaces and trying to split these
spaces?
Let me explain it to you.
Using an example, suppose I have three variables.
Excellent x2 and the category or the class to which that observation belongs.
These x1, x2 and classes can be anything related to your business, and Edu, x1 and X2 could be height
and weight so students and classes could be weathered.
The student passes or fails.
A sports test X1 and X2 could be the results of two medical tests.
Besides which, we may be trying to classify whether the patient has a heart disease or not.
It could be anything.
Basically we have to predictor variables and one variable is to be predicted, which is also known as
the response variable.
So X1 and X2 are the predictor variables and category is the response variable.
Since we have two predictor variables, we can plot the observations on a two dimensional space such
as this.
We can have X one on the x axis, x2 on the Y axis, and Galut of each point will tell us to which class
that particular point belongs.
So all the blue points belong to one class and all these purple points belong to another class.
I think you can connect the daughter between our hyper plane discussion and this example.
This is basically a p dimensional space here being equal to two, because we have two predictive variables.
And this is a two dimensional space.
We want a hyper plane, which will be a line for this two dimensional space.
So we want such a hyper plane which can divide this space into two parts such that all the blue points
are in one part and all the purple points are in another part.
If I am able to find this iBOT plane, I will have my classified model with me.
Any point which falls on this side of this hyper plane will be classified as blue or class one.
And anything that falls on this side of the hyper plane will be classified as purple or glass to simple,
right?
It is simple to know.
Let's dig deeper in the next.
We do.