Consider the data set 10, 20, 30, and 40. We would like to separate this data set into two groups 2. (a) By using k-means approach, start with clusters 110,40), and (20,30), and continue till the algorithm converges (b) By using k-means approach, start with clusters(10,30and (20,40) and continue till the algorithm converges (c) Solve the same problem by using the Otsu method.

2. a)
The data set is provided {10,20,30,40}
Assume the two mean point for the given cluster let us assume M1 = 20 and M2 = 40
Using Euclidean distance find the distance i.e. dist(x,a) = Sqrt(x-a)2
Now D1 is the distance from M1
and D2 is the distance from M2
D1(10) = sqrt(100) = 10 cluster :1
D2(10) = sqrt(900) = 30
D1(30) = sqrt(100) = 10
D2(30) = sqrt(100) = 10 cluster :2
Minimum distance are considered
Thus the clusters are:
C1= {10,20}
c2 = {30,40}
You can generate this way cluster if it is not provided.
However we have been provided with the cluster c1={10,40} and c2= {20,30}
Calculate the mean for the above clusters:
M1 = (10+40)/2 = 25
M2 = (20+30) / 2 = 25
Now recalculate the distance with M1 = 25 and M2= 25
D(10) = sqrt (225) = 15
D(20) = sqrt (625) = 25
D(30) = sqrt(25) = 5
D(40)= sqrt(225) = 15
As the value of M1 and M2 is equal so all the distances we have marked with D only
As all of them equal we are assuming C1= {10,20} and C2 = {30,40}
so the updated mean value will be M1 = 15 and M2 = 5
Now again recalculate the distance with M1 and M2
D1(10)= 5
D2(10)= 5
D1(20)= 5
D2(20)=15
D1(30) = 15
D2(30)= 25
D1(40)= 25
D2(40)= 35
So new clusters C1 = {30,40} and C2= {10,20}
When we will find no moments among the itemset of the clusters thus it will be considered as the final cluster.
 
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