Support Vector Machines — Lecture series — Hyperplanes
In the previous post, we talked about the idea of linear separability and what it means. In this post, we will be talking about the concept of hyperplanes.
Learning objective:
Understand what hyperplanes are.
Main question:
Before we even delve into the concept of a “hyperplane”, we have to first ask ourselves the following question, “what is a plane?”.
To help answer this initial question, take a look at the image in Fig. 1:
In our three dimensional world, any two dimensional surface that exists within it (like the surface depicted in Fig 1)and extends in all directions indefinitely is referred to as a “plane”. A nice visual representation of a plane is to think of the tiled-floor in a hall. Even though the tiled-floor does not extend indefinitely, it certainly looks two-dimensional compared to the other objects in the hall, such as a piece of furniture that may be placed on the tiled-floor.
Well with this explanation of a plane, what then is a “hyper” plane?
Let’s consider the word “hyper” for a second. What does this word mean?
According to the quick google search that I just performed, the word “hyper” means something that is “over”, “above” and “beyond”. If we combine the respective meanings of the words “hyper” and “plane”, we get the sense that a “hyperplane” is a plane that is “over”, “above” and “beyond”. And this intuitive meaning is right!
We can informally describe a hyperplane as a plane with a dimension of n that exists in a space that has a dimension of n + 1. For instance, a plane that has three dimensions that exists in a four-dimensional space can be referred to as a hyperplane.
In the next post we will be looking at the equation of a hyperplane.