Numerical Computing with Python

K-means working methodology from first principles

The k-means working methodology is illustrated in the following example in which 12 instances are considered with their X and Y values. The task is to determine the optimal clusters out of the data.

Instance	X	Y
1	7	8
2	2	4
3	6	4
4	3	2
5	6	5
6	5	7
7	3	3
8	1	4
9	5	4
10	7	7
11	7	6
12	2	1

After plotting the data points on a 2D chart, we can see that roughly two clusters are possible, where below-left is the first cluster and the top-right is another cluster, but in many practical cases, there would be so many variables (or dimensions) that, we cannot simply visualize them. Hence, we need ...