Support Vector Machine(SVM) in Data Science

A support vector machine is a popular Machine Learning tool.

• they can be used both for classification and regression

• they can be used for a linear and non-linear models

We will consider a binary classification problem with positive y = +1 and negative y = -1 classes.

Objective

The goal of a Support vector machine is to separate the two classes using a line that

maximizes the minimal distance (margin) of the data to the decision boundary.

There are two types of large margin classification:

hard margin classification:

• we do not tolerate any data points in the margin

• only works on linearly separable data

• sensitive to outliers (a single point can change the data from separable to nonseparable)

soft margin classification:

• we tolerate a small amount of data in the margin region or even on the wrong side of the margin

For our linear model the value

is proportional to the distance to the z=0 curve:

By rescaling "w" we change the relationship between the distance and the value of z.

In an SMV we declare our margin to be between z = 1 and z=-1 the value of w0, "w".

that

• minimizes the amount of data in the margin (margin violation)

• maximizes the width of the margin

The two goals can be in conflict!

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