Single Linkage Manhattan Distance Hierarchical Classification

The classification hierarchy will use Manhattan distance.
The data we will use is as follows :

The initial stage is to calculate data X and data Y.
At this stage, the calculation method is different from the others.
The calculation stages are as follows:
 

• D1,D1 means (X1-X1) + (Y1-Y1) ^ 1/C1 (using manhattan distance)
• D1,D2 means (X1-X2) + (Y1-Y2) ^ 1/C1 (using manhattan distance)
• D1,D3 means (X1-X3) + (Y1-Y3) ^ 1/C1 (using manhattan distance)
• D1,D4 means (X1-X4) + (Y1-Y4) ^ 1/C1 (using manhattan distance)
• D1,D5 means (X1-X5) + (Y1-Y5) ^ 1/C1 (using manhattan distance)
• D2,D2 means (X2-X2) + (Y2-Y2) ^ 1/C1 (using manhattan distance)
• D2,D3 means (X2-X3) + (Y2-Y3) ^ 1/C1 (using manhattan distance)
• D2,D4 means (X2-X4) + (Y2-Y4) ^ 1/C1 (using manhattan distance)
• D2,D5 means (X2-X5) + (Y2-Y5) ^ 1/C1 (using manhattan distance)
• D3,D3 means (X3-X3) + (Y3-Y3) ^ 1/C1 (using manhattan distance)
• D3,D4 means (X4-X4) + (Y4-Y4) ^ 1/C1 (using manhattan distance)
• D3,D5 means (X5-X5) + (Y5-Y5) ^ 1/C1 (using manhattan distance)
• D4,D4 means (X4-X4) + (Y4-Y4) ^ 1/C1 (using manhattan distance)
• D4,D5 means (X4-X5) + (Y4-Y5) ^ 1/C1 (using manhattan distance)
• D5,D5 means (X5-X5) + (Y5-Y5) ^ 1/C1 (using manhattan distance)

The results are as follows:

Next is to create a matrix diagram:

From the matrix above, we will choose the smallest result except 0 and it turns out that the smallest value is 1 which is owned by data 4 to 5 and 5 to 4.
We will combine the data to form the following:

• D(45)1
• D(45)2
• D(45)3

The results obtained are as follows:

After getting the data, the smallest value is selected to form a matrix as follows:

After that, the smallest data from the data above is selected again, so that what is obtained is as follows:

• D(452)1
• D(452)3

The results obtained are as follows:

After obtaining the data, the smallest value is selected to form a matrix as follows:

After that, the smallest data from the data above is selected again, so that what is obtained is as follows:

• D(4523)1

 
The results obtained are as follows:

After getting the data, the smallest value is selected to form a matrix as follows:

From the results above, we can create a diagram, so that the diagram is formed as follows: