First, we need to understand what qualifies for a separating hyperplane. In the following example, hyperplane C is the only correct one, as it successfully segregates observations by their labels, while hyperplanes A and B fail:
This is an easy observation. Let's express a separating hyperplane in a formal or mathematical way.
In a two-dimensional space, a line can be defined by a slope vector w (represented as a two-dimensional vector), and an intercept b. Similarly, in a space of n dimensions, a hyperplane can be defined by an n-dimensional vector w, and an intercept b. Any data point x on the ...
