Point P1 2 4 P2 4 P3 P4

Computer Networking: A Top-Down Approach (7th Edition)
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5. Data Matrix
Point
X
P1
P2
4
2
P3
6
3
P4
5
A. Calculate the Eucilidean distance between all points in the two-dimensional data set, then ex-
press it in a distance matrix. (show the method)\
B. Determine the City Block Distance matrix and the Supremum Distance matrix for the data set.
Transcribed Image Text:5. Data Matrix Point X P1 P2 4 2 P3 6 3 P4 5 A. Calculate the Eucilidean distance between all points in the two-dimensional data set, then ex- press it in a distance matrix. (show the method)\ B. Determine the City Block Distance matrix and the Supremum Distance matrix for the data set.
Expert Solution
Step 1

As per our policy we are allowed to solve only first sub part in multi part system.so please upload other question again.

Formula to calculate Euclidean distance is

D=√[ (x – x)2 + (y– y)2

So to calculate distance between each point we well create a 4 X 4 matrix

Euclidean distance

Distance between P1 and P1 will be zero similarly all diagonal distance will be 0.

Distance between P1 and P2 will be calculated as 

D=√[ (x – x)2 + (y– y)2

D=√[ (4 – 2)2 + (2– 4)2

D=√[ 4 + 4] 

D=2.83

Similarly we can calculate distance for all points 

Value of all distance is shown below in a matrix

Distance between P1 and P3 will be calculated as 

D=√[ (x – x)2 + (y– y)2

D=√[ (6 – 2)2 + (3– 4)2

D=√[ 16 + 1] 

D=4.12

Distance between P1 and P4 will be calculated as 

D=√[ (x – x)2 + (y– y)2

D=√[ (5 – 2)2 + (1– 4)2

D=√[ 9 + 9] 

D=4.24 

Distance between P2 and P3 will be calculated as 

D=√[ (x – x)2 + (y– y)2

D=√[ (6 – 4)2 + (3– 2)2

D=√[ 4 + 1] 

D=2.23

Distance between P2 and P4 will be calculated as 

D=√[ (x – x)2 + (y– y)2

D=√[ (5 – 4)2 + (1– 2)2

D=√[ 1 + 1] 

D=1.41

 

Distance between P3 and P4 will be calculated as 

D=√[ (x – x)2 + (y– y)2

D=√[ (5 – 6)2 + (1– 3)2

D=√[ 1 + 4] 

D=2.23

 

 

 

 

 

 

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