Question 1 Table 1 shows ten products of shoes imported by a shoe shop. The shop owner asks you to perform cluster analy

[answerhappygod]

Question 1
Table 1 shows ten products of shoes imported by a shoe shop. The shop owner asks you to perform cluster analysis to determine different groups of products. The shop owner considers two criteria, such as unit price and coziness rating, for each product of shoes. You have decided to use k-means algorithm to create two clusters. The initial centroids are given in Table 2.
Table 1. Shoes of different styles.
Shoes
Unit Price ($)
Coziness Rating
P1
100
8
P2
110
5
P3
100
3
P4
105
4
P5
98
3.5
P6
101
8
P7
102
7
P8
106
3.5
P9
108
2
P10
97
3.2
Table 2. Initial Centroids of the Clusters
Cluster
Unit Price ($)
Coziness Rating
A
100
6
B
103
8
Question 2
Table 3 shows a distance matrix of 5 points. Perform hierarchical clustering using “MIN” (single link), list the merge operations and updated matrices step by step. Show the results by drawing a dendrogram. The dendrogram should clearly show the order in which the points are merged.
Table 3. Distance Matrix
P1
P2
P3
P4
P5
P1
0.00
1.00
1.60
2.50
1.80
P2
1.00
0.00
0.60
2.80
2.50
P3
1.60
0.60
0.00
2.40
2.20
P4
2.50
2.80
2.40
0.00
1.20
P5
1.80
2.50
2.20
1.20
0.00
Question 1 Table 1 shows ten products of shoes imported by a shoe shop. The shop owner asks you to perform cluster analysis to determine different groups of products. The shop owner considers two criteria, such as unit price and coziness rating, for each product of shoes. You have decided to use k- means algorithm to create two clusters. The initial centroids are given in Table 2. Table 1. Shoes of different styles. Shoes Unit Price (s) Coziness Rating PI 100 P2 110 P3 100 P4 105 PS 98 P6 101 P7 102 P8 106 P9 108 PIO 97 5 3 4 3.5 8 7 3.5 2 3.2 Table 2. Initial Centroids of the Clusters Cluster Unit Price (5) Coziness Rating А 100 B 103 a) Calculate the Euclidean distance between each shoe and the centroids of the two clusters b) Based on the results in part a), assign each shoe to the cluster with the closest centroid. c) Update the centroids of the two clusters. d) Calculate the Euclidean distance between each shoe and the centroids of the two updated clusters. Assign each shoe to the cluster with the closest centroid. Update the centroids of the two clusters. e) Calculate the Euclidean distance between each shoe and the centroids of the two updated clusters obtained in part d). Assign each shoe to the cluster with the closest centroid. Update the centroids of the two clusters.
f) Calculate the Euclidean distance between each shoe and the centroids of the two updated clusters obtained in part e). Assign each shoe to the cluster with the closest centroid. Is it necessary to update the centroids of the two clusters? If yes, find the updated centroids of the two clusters. g) Find the sum of squared error (SSE) of the clustering. Question 2 Table 3 shows a distance matrix of 5 points. Perform hierarchical clustering using “MIN” (single link), list the merge operations and updated matrices step by step. Show the results by drawing a dendrogram. The dendrogram should clearly show the order in which the points are merged. Table 3. Distance Matrix P1 P2 P3 P4 P5 P110.00 1.00 1.602.50 1.80 P2/1.000.000.602.80|2.50 P3/1.600.600.00 2.402.20 P42.50 2.80 2.400.00 1.20 P51.802.50 2.20 1.200.00