Mathematics behind clustering

Earlier in this chapter, we discussed how a measure of similarity or dissimilarity is needed for the purpose of clustering observations. In this section, we will see what those measures are and how they are used.

Distances between two observations

If we consider each observation as a point in an n-dimensional space, where n is the number of columns in the dataset, one can calculate the mathematical distance between the points. The lesser the distance, the more similar they are. The points that are less distant to each other will be clubbed together.

Now, there are many ways of calculating distances and different algorithms use different methods of calculating distance. Let us see the different methods with a few examples. Let us consider a sample dataset of 10 observations with three variables, each to illustrate the distance better. The following dataset contains percentage marks obtained by 10 students in English, Maths, and Science:

Student	English...