CODEWITHSUNDEEP
pythonclassificationsvm
Shiva RD
Shiva RD

Reputation: 73

How is classification mathematically done in SVM if target is labeled as 0 and 1?

My dataset has feature columns and a target label of 0 and 1.

When I use SVM classifier for binary classification it predicts well.

But my question is how is it mathematically predicted.?

The marginal hyperplanes H1 and H2 have the equations: W^T X +b >= 1

meaning if greater than +1 it falls in one class. And if less than -1, it falls in another class.

But we have given the target label 0 and 1.

How actually is it done mathematically?

Anyone expert please.....

Upvotes: 1

Views: 785

Answers (1)

Epimetheus
Epimetheus

Reputation: 393

Basically, SVM wants to find the optimal hyperplane that splits the datapoints in such way that the margin between the closest datapoints of each class (the so-called support vectors) is maximized. This all breaks down to the following Lagrangian optimization problem: enter image description here

  • w:vector that determines the optimum hyperplane ( for intuition, make yourself familiar with the geometrical meaning of a dot product)

  • (w^T∙x_i+b) is a scalar and displays the geometrical distance between single datapoint x_i and the maximum margin hyperplane

  • b is a bias vector ( I think it comes from indetermined integral in derivation of SVM) more on that you can find here: University Stanford -Computer Science Lecture 3-SVM

  • λ_i the Lagrangian multiplier

  • y_i the normalized classification boundary

Solving the optimization problem leads to all necessary parameters of w, b, and lambda.

To answer you quesiton in one sentence: The class boundaries [-1,1] are set arbitrarily. It is really just definition. enter image description here

The labels of your binary data [0;1] (so-called dummy varaibles) have nothing to with the boundaries. It is just a convenient way to label binary data. The labels are only needed to link the features to its corresponding class or category.

The only non paramter in Formula (8) is x_i , your datapoint in feature space.

At least thats how I understand SVM. Feel free to correct me if I am wrong or unprecise.

Upvotes: 1

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