Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a collected data on 5 different characteristics. Amanda has applied k-means clustering to this data for k

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Question No: Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a collected data on 5 different characteristics. Amanda has applied k-means clustering to this data for = 2. Given the following data:
                                                                  Table 5.1

Observations

X

Y

1

20

18

2

8

20

3

36

26

4

22

12

5

14

4


d) Visually represent the clusters of both parts (b) and (c).

Note: I have already attach "B" and "c" part with images that have been solve. Only do "D" part  for solve.

b)
Let the Initial two clusters be (1, 2) and (3,4, 5)
The centrolds for two clusters are calculated as shown below
For Cluster (1,2)
X = = 14
Y =
= 19
For Cluster (3,4,5)
X = J6+2tl4 = 24
3
The centrold for two clusters are (14,19) for Cluster-1 (1,2) and (24,14) for Cluster-2 (3,4,5).
c)
The distance of observation from both cluster centrold Is calculated below
Observation (X, Y)
Centroid – I
Centroid – 2
V(20 - 24) + (18 – 14)2 = 5. 66
V(8 - 24) + (20 – 14) = 17.09
(20, 18)
V(20 – 14)2 + (18 - 19)? = 6. 08
(8, 20)
V(8 – 14) + (20 – 19) = 6. 08
(36, 26)
(36 14)2 + (26 - 19)2 = 23.08
(36-24) +(26- 14) = 16. 97
(22, 12) V(22 - 14) + (12 – 19) = 10. 63 V(22- 24 + (12 – 14) = 2. 83
V(14 – 24 + (4 – 14) = 14. 14
4
5
(14, 4)
V(14 – 14) + (4 – 19) = 15
Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). So the clusters are newly
formed as shown below
Cluster-1 = {2)
Cluster-2= {1,3,4, 5}
The centrolds for two clusters are calculated as shown below
For Cluster (2)
X = 8
Y = 20
For Cluster (1,3,4,5)
X = 0.36+22+ 14
= 23
4
Y =
4
Transcribed Image Text:b) Let the Initial two clusters be (1, 2) and (3,4, 5) The centrolds for two clusters are calculated as shown below For Cluster (1,2) X = = 14 Y = = 19 For Cluster (3,4,5) X = J6+2tl4 = 24 3 The centrold for two clusters are (14,19) for Cluster-1 (1,2) and (24,14) for Cluster-2 (3,4,5). c) The distance of observation from both cluster centrold Is calculated below Observation (X, Y) Centroid – I Centroid – 2 V(20 - 24) + (18 – 14)2 = 5. 66 V(8 - 24) + (20 – 14) = 17.09 (20, 18) V(20 – 14)2 + (18 - 19)? = 6. 08 (8, 20) V(8 – 14) + (20 – 19) = 6. 08 (36, 26) (36 14)2 + (26 - 19)2 = 23.08 (36-24) +(26- 14) = 16. 97 (22, 12) V(22 - 14) + (12 – 19) = 10. 63 V(22- 24 + (12 – 14) = 2. 83 V(14 – 24 + (4 – 14) = 14. 14 4 5 (14, 4) V(14 – 14) + (4 – 19) = 15 Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). So the clusters are newly formed as shown below Cluster-1 = {2) Cluster-2= {1,3,4, 5} The centrolds for two clusters are calculated as shown below For Cluster (2) X = 8 Y = 20 For Cluster (1,3,4,5) X = 0.36+22+ 14 = 23 4 Y = 4
The centrold for two clusters are (8,20) for Cluster-1 (2) and (23,15) for Cluster-2 (1,3,4,5).
The distance of observation from both cluster centrold Is calculated below
Observation (X, Y)
Centroid – 1
Centroid – 2
I
(20, 18) V(20 - 8) + (18 – 20) = 12. 16 V(20-23)2 + (18 – 15) = 4. 24
(8, 20)
V(8 - 8) + (20 – 20 = 0
V(8 – 23)2 + (20 – 15) = 15. 81
(36, 26)
(36 – 8)* + (26 – 20) = 28. 64 V(36 – 23) + (26 – 15) = 17.03
(22, 12) V(22 – 8)* + (12 – 20) = 16. 12 V(22 – 23)2 +(12 – 15)2 = 3. 16
V14 – 8)* + (4 – 20) = 17.09 V(14 – 23) + (4 – 15) = 14.21
V(14-23)+(4-15) - 14.21
5
(14, 4)
Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). Thus the final clusters are
Cluster-1 = {2)
Cluster-2 = {1,3,4,5}
3.
Transcribed Image Text:The centrold for two clusters are (8,20) for Cluster-1 (2) and (23,15) for Cluster-2 (1,3,4,5). The distance of observation from both cluster centrold Is calculated below Observation (X, Y) Centroid – 1 Centroid – 2 I (20, 18) V(20 - 8) + (18 – 20) = 12. 16 V(20-23)2 + (18 – 15) = 4. 24 (8, 20) V(8 - 8) + (20 – 20 = 0 V(8 – 23)2 + (20 – 15) = 15. 81 (36, 26) (36 – 8)* + (26 – 20) = 28. 64 V(36 – 23) + (26 – 15) = 17.03 (22, 12) V(22 – 8)* + (12 – 20) = 16. 12 V(22 – 23)2 +(12 – 15)2 = 3. 16 V14 – 8)* + (4 – 20) = 17.09 V(14 – 23) + (4 – 15) = 14.21 V(14-23)+(4-15) - 14.21 5 (14, 4) Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). Thus the final clusters are Cluster-1 = {2) Cluster-2 = {1,3,4,5} 3.
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