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Consider the data given below. Create adjacency matrix. Apply single link algorithm to cluster the given data set and draw the dendogram.
Object Attribute 1 (X) Attribute 2 (Y)
A 2 2
B 3 2
C 1 1
D 3 1
E 1.5 1.5
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Solution:

Object Attribute 1 (X) Attribute 2 (Y)
A 2 2
B 3 2
C 1 1
D 3 1
E 1.5 1.5

For simplicity we can find the adjacency matrix which gives distances of all object from each other. Using Euclidean distance we have

\begin{aligned} \mathrm{D}(\mathrm{i}, \mathrm{j}) &=\sqrt{\left|\mathrm{x}_{2}-\mathrm{x}_{1}\right|^{2}+\left|\mathrm{y}_{2}-\mathrm{y}_{1}\right|^{2}} \\ \mathrm{D}(\mathrm{A}, \mathrm{B}) &=\sqrt{(2-3)^{2}+(2-2)^{2}}=1 \end{aligned}

Similarly we can compute for the rest.

A B C D E
A 0
B 1 0
C 1.41 2.24 0
D 1.41 1 2 0
E 1.58 2.12 0.71 1.58 0

step 1: Since $C, E$ is minimum we can combine clusters $C, E$

- A B (C,E) D
A 0
B 1 0
C 1.41 2.12 0
D 1.41 1 1.58 0

Step 2: Now $\mathrm{A}$ and $\mathrm{B}$ is having minimum value therefore we merge these two clusters.

- (A,B) (C,E) D
(A,B) 0
(C,E) 1.41 0
D 1 1.58 0

Step 3 : Cluster $(\mathrm{A}, \mathrm{B})$ and $\mathrm{D}$ can be merged together as they are having minimum distance value

- (A,B,D) (C,E)
(A,B,D) 0
(C,E) 1.41 0

Step 4 : In the last step there are only two clusters to be combined they are, $(\mathrm{A}, \mathrm{B}, \mathrm{D})$ and $(\mathrm{C}, \mathrm{E})$

Now the final dendrogram is 