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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