9.1 Support vector machines
QSVMs are actually particular cases of Support Vector Machines (abbreviated as SVMs). In this section, we will explore how these SVMs work and how they’re used in machine learning. We will do so by first motivating the SVM formalism with some simple examples, and then building up from there: all the way up into how SVMs can be used to tackle complex classification problems with the kernel trick.
9.1.1 The simplest classifier you could think of
Let us forget about data for a moment and begin by considering a very naive problem. Let’s say that we want to build a very simple classifier on the real line. In order to do this, all we have to do is split the real number line into two disjoint categories in such a way that any number belong to exactly one of these two categories. Thus, if we are given any input (a real number), our classifier will return the category to which it belongs.
What would be the easiest way in which you could do this? Odds...
