Consider the following set of two-dimensional records:

Question

Also consider two different clustering schemes: (1) where Cluster 1 contains records {1, 2, 3} and Cluster 2 contains records {4, 5, 6} and (2) where Cluster 1 contains records {1, 6} and Cluster 2 contains records {2, 3, 4, 5}. Which scheme is better and why?

Answer 1

Compare the error of the two clustering schemes. The scheme with the
smallest error is better.

For SCHEME (1) we have C1 = {1,2,3} and C2 = {4,5,6}
M1 = ((8+5+2)/3, (4+4+4)/3) = (5,4)

2 2 2 2 2 2
C1_error = (8-5) + (4-4) + (5-5) (4-4) + (2-5) + (4-4)
= 18

For C2 we have
M2 = ((2+2+8)/3, (6+8+6)/3) = (4,6.66)

2 2 2 2 2 2
C2_error = (2-4) + (6-6.66) + (2-4) (8-6.66) + (8-4) + (6-6.66)
= 26.67

C1_error + C2_error = 44.67


For SCHEME (2) we have C1 = {1,6} and C2 = {2,3,4,5}
M1 = ((8+8)/2, (4+6)/2) = (8,5)

2 2 2 2
C1_error = (8-8) + (4-5) + (8-8) (6-5)
= 2

For C2 we have
M2 = ((5+2+2+2)/4, (4+4+6+8)/4) = (2.75,5.5)

C2_error =
2 2 2 2 2 2 2 2
(5-2.75) +(4-5.5) +(2-2.75) +(4-5.5) +(2-2.75) +(6-5.5) +(2-2.75) +(8-5.5)

= 17.74

C1_error + C2_error = 19.74


SCHEME 2 is better since the error associated with it is less than that
of SCHEME (1).