K-means Clustering Methods, Exercises of Data Mining

1. (a). Use the k-means algorithm and calculate the distance for each centroids from a data

point and the data point having minimum distance from the centroid of a cluster is assign to

that particular cluster center and calculate the mean value for that cluster center. Show the

result for each iteration to cluster the following 8 samples into 3 clusters: A1(2,10),

A2(2,5), A3(8,5), B1(5, 8), B2(7,5), B3(6,4), C1(1,2), C2(4,9). Suppose that the initial

centroids (centers of each cluster) are A1(2,10), B1(5,8), C1(1,2). Run the k-means

algorithm for each iteration. At the end of this iteration show:

1. The new clusters and update the centroids of the new clusters;

distance from the centroid of a cluster is assign to that particular cluster center and calculate the mean value

for that cluster center.

Two points (x1,y1), (x2,y2)

Euclidean distance Formula: =√(x2-x1)2 + (y2-y1)2

or = |x2-x1| + |y2-y1|

Mean Formula: ((x1+x2) / 2, (y1+y2) / 2).

1ST ROW:

Distance calculate between the A2 data point and the Centroids A1, B1, C1

Distance between A2(2,5) & A1(2,10) = |2-2| + |5-10| = 0+5 = 5

Distance between A2(2,5) & B1(5,8) = |2-5| + |5-8| = 3+3 = 6

Distance calculate between the A3 data point and the Centroids A1, B1, C1

Distance between A3(8,5) & A1(2,10) = 11

Distance between A3(8,5) & B1(5,8) = 6

Distance between A3(8,5) & C1(1.5,3.5) = 8

The A3 nearby Cluster Center is B1.

Then we need to calculate the mean value between the A3 and B1.

B1 Mean value = (6.5, 6.5)

Then we need to update the centroid B1 value as (6.5, 6.5).

3RD ROW:

Distance calculate between the B2 data point and the Centroids A1, B1, C1