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Support Vector Machine(SVM) in Machine Learning

Support vector machine (SVM) algorithms are used in classification.
Classification can be viewed as the task of separating classes in feature space.

Here we select 3 support Vectors to start with.
They are S1,S2  and S3.

Here we will use vectors augmented with a 1 as a bias input, and for clarity we will differentiate these with an over-tilde. 
That is:

Now we need to find 3 parameters ɑ12 and ɑ3 based on the following 3 linear equations:

Let's substitute the values for Š1,Ŝ2 and Š3 in the above equations.

After simplification we get:

Simplifying the above 3 simultaneous equations we get: ɑ12= -3.5 and ɑ3=3.5.

The hyper plane that discriminates the positive class from the negative class is give by:
Substituting the values we get:

Our vectors are augmented with a bias.
Hence we can equate the entry Ŵ as the hyper plane with an offset b.
Therefore the separating hyper plane equation y = w𝓍 + b with w = {1 0} and offset b = -3.

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