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.
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".
minimizes the amount of data in the margin (margin violation)
maximizes the width of the margin
The two goals can be in conflict!