Defining the Clustering Problem

We shall define the clustering problem so that we will be able to find similarities between our data points. For instance, suppose we have a dataset that consists of points. Clustering helps us understand this structure by describing how these points are distributed.

Let's look at an example of data points in a two-dimensional space in Figure 5.1:

Figure 5.1: Data points in a two-dimensional space

Now, have a look, at Figure 5.2. It is evident that there are three clusters:

Figure 5.2: Three clusters formed using the data points in a two-dimensional space

The three clusters were easy to detect because the points are close to one another. Here, you can see that clustering determines the data points that are close to each other. You may have also noticed that the data points M1, O1, and N1 do not belong to any cluster; these are the outlier points. The clustering algorithm you build should be prepared...