Question

For k-means clustering, what will be the cluster centroids for the following 2 clusters? C1:{(3,5),(5,4),(4,6)} :{(6,0),(8,1),(7,2)}

A) (5,5) and (7,1)
B) (4,5) and (7,1)
C) (4,5) and (7,2)
D) (5,5) and (8,1)

Answer 1

To find the cluster centroids in k-means clustering, you average the coordinates of the points within each cluster. For C1, the centroid is (4,5) and for C2, the centroid is (7,1). Thus, the correct answer is B) (4,5) and (7,1).

Step-by-step explanation:

To calculate the cluster centroids in k-means clustering, we need to take the average of the points in each cluster. For cluster C1, which contains the points (3,5), (5,4), and (4,6), we calculate the average for each dimension separately:

1. Add the x-coordinates: 3 + 5 + 4 = 12.
2. Divide by the number of points in the cluster: 12 / 3 = 4.
3. Add the y-coordinates: 5 + 4 + 6 = 15.
4. Divide by the number of points: 15 / 3 = 5.

So, the centroid for C1 is (4,5).

For the second cluster C2, containing the points (6,0), (8,1), and (7,2):

1. Add the x-coordinates: 6 + 8 + 7 = 21.
2. Divide by the number of points in the cluster: 21 / 3 = 7.
3. Add the y-coordinates: 0 + 1 + 2 = 3.
4. Divide by the number of points: 3 / 3 = 1.

The centroid for C2 is (7,1). The correct answer is B) (4,5) and (7,1).