Machine Learning Algorithms

Linear classification

Let's consider a generic linear classification problem with two classes. In the following figure, there's an example:

Our goal is to find an optimal hyperplane, which separates the two classes. In multi-class problems, the strategy one-vs-all is normally adopted, so the discussion can be focused only on binary classifications. Suppose we have the following dataset:

This dataset is associated with the following target set:

We can now define a weight vector made of m continuous components:

We can also define the quantity ...