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 ...

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