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dimulka [17.4K]
3 years ago
7

Consider a set of one-dimensional points: 6, 12, 18, 24, 30, 42, 48.

Mathematics
1 answer:
Vinvika [58]3 years ago
6 0

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 = (18-6)^{2}+(18-12)^{2}+(18-18)^{2}+(18-24)^{2}+(18-30)^{2}+(45-42)^{2}+(45-48)^{2}=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 = (15-6)^{2}+(15-12)^{2}+(15-18)^{2}+(15-24)^{2}+(40-30)^{2}+(40-42)^{2}+(40-48)^{2}=348

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