Today, I would give a very simple explanation of the concept of linear seperator and hyperplane.

This is would be a very basic and simple, easy to understand explanation, just to help you pass your exam or a test.☺

**Content**

- What is Linear Seperability?
- Formal Definition of Linear Separability
- What is a Linear Separator?
- What is a Hyperplane?
- That is it!

### 1. What is a Linear Separability?

To answer this quesion we need to first understand the concept of linear seperability.

First, the concept of linear seperation applies to a set of points.

The two sets of points are said to be linearly seperable if a line can be drawn that seperates the points such that a set points is on one side of the line and anothe set of points is on the other side of the line.

Figure 1: Can you figure it out?

Now take a look at Figure 1. Can figure out which set of points are linearly seperable?

For sure, we could see that the answer is Set 3.

### 2. Formal Definition of Linear Separation

Assuming that the blue data sets represents set of point X0

The red data sets represents set of point X1

Then the two sets X0 and X1 are linearly seperable if there exist n+1 real numbers:

w1, w2, ..., wn, k

such that every point in X0 satisfies the relation

and every point in X1 satisfies the relation

### 3. What is a Linear Seperator?

From what we've discussed so far, can you say what a Linear Seperator is? It is simply the plane/line that sepearates the two sets of data!

(I must say, that formal definitions make simple concepts appear difficult)

But let's take a formal definition

A linear seperator is a a vector-threshold pair, (w, k) that satisfies the two relations given above

### 4. What is a Hyperplane?

As I mentioned, sometimes the terms used makes the concept appear complicated. The concepts of hyperplane is very simple: A hyperplane is just a plane that is one dimension less than the current space being considered.

**Quiz****1**: If a space is a 3-dimensional space, what would be the hyperplanes?

*Answers*: 2-dimensional plane

**Quiz 2**: If a a plane is two-dimensional, what would be the hyperplanes?

*Answer*: 1-dimensional lines

### 5. Thats is it!

As I mentioned, this is a very basic and simple explanation to help you pass your test. But if you would like to have more detailed explanation, let me know in the comment box below or in the form to the left of this page.