Answer:
1) With initial centroids 10-40, final clusters are
first cluster (6,12,18,24,30)
second cluster (42,48)
And the Sum of Squared Errors (SSE) for the clustering result is 378
2) With initial centroids 10-20, final clusters are
first cluster (6,12,18,24)
second cluster (30,42,48)
And the Sum of Squared Errors (SSE) for the clustering result is 348
Step-by-step explanation:
K-means works as follows
- the points will be clustered according to their distance to the centroids.
- Then centroids are updated as the cluster means.
- This process continues until clusters doesn't change anymore
1) <u><em>initial centroids</em></u> 10-40
first cluster (6,12,18,24) mean:15
second cluster (30,42,48) mean:40
<u><em>new centroids</em></u> 15-40
first cluster (6,12,18,24,30) mean:18
second cluster (42,48) mean:45
<u><em>final centroids</em></u> 18-45
first cluster (6,12,18,24,30) mean:18
second cluster (42,48) mean:45
Sum of Squared errors = +
+
+
+
+
+
=378
2)<u><em>initial centroids</em></u> 10-20
first cluster (6,12) mean:9
second cluster (18,24,30,42,48) mean:32.4
<u><em>new centroids</em></u> 9-32.4
first cluster (6,12,18) mean:12
second cluster (24,30,42,48) mean:36
<u><em>new centroids</em></u> 12-36
first cluster (6,12,18,24) mean:15
second cluster (30,42,48) mean:40
<u><em>final centroids</em></u> 15-40
first cluster (6,12,18,24) mean:15
second cluster (30,42,48) mean:40
Sum of Squared errors = +
+
+
+
+
+
=348