Support Vector Machines — Lecture series — What is a vector?

Since the concept of vectors is central to the understanding of support vector machines, we need to talk about them.

If you already have a basic understanding of vectors, the first series of posts will serve as a great revision of ideas that you are already familiar with.

If you however have no idea what a vector is, these posts will help you to get comfortable with the idea.

Side note: To make concepts as easy to understand as possible without using all of the usual mathematical lingo, I would be using fun examples and scenarios to explain them.

Learning objective:

Understand what a vector is

The main question:

If you were the stick figure drawn in Fig 1 below (pardon my drawing, I tried my best :) ) and you were asked to move from point A to point B blindfolded, how would you do it?

Fig. 1

Well, since you are blindfolded and you can only ask for assistance and listen for directions, a good first question to ask is how many steps it would take for you to move from point A to point B.

Consider the image in Fig 2 below:

Fig. 2

If you are told that it would take 10 steps to move from point A to B, you would have received good but incomplete information. This is because, if you move 10 steps in the opposite direction away from B, you will never get to B.

Therefore, a good next question to ask is, 10 steps in what direction?

Consider the image in Fig 3 below:

Fig. 3

In the Fig 3, you will see that point B is located at a position which is 4.5 units on the x axis and 4.5 units on the y axis. Hence, if you move 10 steps in this direction, you will eventually get to point B.

The mathematical term which is used to represent any instance that has both a magnitude (which in this case is 10 steps) and a direction (which in this case is 4.5 units on the x axis and 4.5 units on the y axis), is referred to as a vector.

In the next post, we will delve a little deeper into the concept of the magnitude of a vector :)