## Welcome to Reproducing Kernel Hilbert Space

We’ll start with the “classic” example. Consider the data plotted in figure 1. Each data point has 3 “properties”: an coordinate, an coordinate and a colour (red or blue). Suppose we want to be able to separate all data points into two groups: red points and blue points. Furthermore, we want to be able to do this *linearly*, i.e. we want to be able to draw a line (or plane or hyperplane) such that all points on one side are blue, all points on the other are red. This is called linear classification.

Suppose for each data point we generate a *representation* of the data point .…