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So we have a two dimensional predicted space and we want to find the hyper plane which can separate

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this space so that each class is in a different part.

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Probably you'd have guessed in such a scenario where the data is perfectly separable.

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We can draw in finite hyper planes.

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Just take any high powered plane and make tiny shifts or tiny rotations and you would get more hyper

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planes.

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Here you can see three such hyper planes in this figure.

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But which of these hyper planes should we choose and why?

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One reasonable choices, selecting that hyper plane, which is farthest from the training observations.

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That is, we have a hyper plane.

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We find the perpendicular distance of all the observations from this hyper plane, the smallest distance

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of these observations is called margin in this figure.

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You can see that this point is the closest to the iBOT plane.

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So the distance of this point from the hyper plane is the margin.

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In other words, margin is the farthest minimum distance between observations of the hyper plane.

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So whichever hyper plane has maximum value of the margin, that hyper plane will be selected.

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And then whatever it is to the left of this plane is classified as blue or class one.

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And whatever it is to the right is classified as purple or class to.

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This is known as maximal margin classifier.

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You can now see what the name stands for.

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Because we choose the hyper plane with maximum value of margin.

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This is called maximal margin classifier.

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Now, I have chosen the hyper plane.

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I broady the hyper plane and the two margins on this graph.

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And we notice that there are three point which lie on the margin.

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If these points were not there, we would have received wider margins.

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These points are called support vectors because in a way, these points are supporting these margin

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boundaries.

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In fact, if you think about it, other points are not important anymore.

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Our classifier is completely dependent only on these support vectors.

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Any slight movement in any of these support vectors would mean that the classifier will change identification

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of such points and classification on the basis of only these few points.

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Is a special characteristic of support vector classifier and machines which separate this technique

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from any other conventional technique.