The k-means clustering algorithm takes as input the number of clusters k and a set of data points, and assigns each data point to one of k clusters. It works by first randomly selecting k data points as initial cluster centroids. It then assigns each remaining point to the closest centroid, and recalculates the centroid positions. This process repeats until the centroids are stable or a stopping criteria is reached. As an example, the document applies k-means to cluster 6 data points into 2 groups, showing the random selection of initial centroids, assignment of points, and recalculation of centroids over multiple steps.

1. Manual Work
E. N. Sathishkumar M.Sc., M.Phil., [Ph.d]

2. K-Means Algorithm
 Input: n objects (or points) and a number k
 Algorithm
1. Randomly place K points into the space represented by the
objects that are being clustered. These points represent
initial group centroids.
2. Assign each object to the group that has the closest
centroid.
3. When all objects have been assigned, recalculate the
positions of the K centroids.
4. Repeat Steps 2 and 3 until the stopping criteria is met.

3. Worked out Example
 Input: Number of Objects = 6, Number of Clusters = 2
 Step-1: Choose random K points and set as cluster centers
C1 = (2, 2) C2 = (3 , 3) 3
No X Y
1 1 1
2 2 3
3 1 2
4 3 3
5 2 2
6 3 1

4.  Step-2: Calculating the distance between objects into cluster
centroids by using Euclidean Distance
4

5. 5

6.  Step-3: Recalculating the position of the centroid
 Step-4: Go back to Step 2, unless the centroids are not
changing.
6
No X Y
1 1 1
2 2 3
3 1 2
4 3 3
5 2 2
6 3 1