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 hyperplane satisfies wx + b = 0. A hyperplane is a separating hyperplane if the following conditions are satisfied:

• For any data point x from one class, it satisfies wx + b > 0
• For any data point x from another class, it satisfies wx + b < 0

However, there can be countless possible solutions for w and b. You can move or rotate hyperplane C to certain extents and it still remains a separating hyperplane. So next, we will learn how to identify the best hyperplane among possible separating hyperplanes.