K-mean Clustering Algorithm

Q. Use the k-mean clustering to solve the problem ? Itemsets ={2,4,10,2,3,20,30,11,25} and Suppose that k=2. With m1=2 and m2=4.                                                                                                                          

Solution:

Let

Cluster : k1=1 and k2=2

M1	M2	K1	K2
2	4	{2,3}	{4,10,11,12,20,25,30}

Recalculate mean m1,m2 with items in k1 ={2,3}  and k2= {4,10,11,12,20,25,30}

Therfore m1 =(2+3)/2  =  2.5                                                                                                                                                                         m2 =(4,10,11,12,20,25,30)/7 = 16

Now we have DistanceMean1 (2.5) ,DistanceMean2 (16)

M1	M2	K1	K2
2	4	{2,3}	{4,10,11,12,20,25,30}
2.5	16	{2,3,4}	{10,11,12,20,25,30}

Recalculate mean m1,m2 with items in k1 ={2,3,4}  and k2= {10,11,12,20,25,30}

Therfore m1 =(2+3+4)/3  =  3                                                                                                                                                                        m2 =(10+11+12+20+25+30)/6 = 18

Now we have DistanceMean1 (3) ,DistanceMean2 (18)      

M1	M2	K1	K2
2	4	{2,3}	{4,10,11,12,20,25,30}
2.5	16	{2,3,4}	{10,11,12,20,25,30}
3	18	{2,3,4,10}	{11,12,20,25,30}

Recalculate mean m1,m2 with items in k1 ={2,3,4,10}  and k2= {11,12,20,25,30}

Therfore m1 =(2+3+4+10)/4  =  4.75                                                                                                                                                                           m2 =(11+12+20+25+30)/5 = 19.6

Now we have DistanceMean1 (4.75) ,DistanceMean2 (19.6)       

M1	M2	K1	K2
2	4	{2,3}	{4,10,11,12,20,25,30}
2.5	16	{2,3,4}	{10,11,12,20,25,30}
3	18	{2,3,4,10}	{11,12,20,25,30}
4.75	19.6	{2,3,4,10,11,12}	{20,25,30}

Recalculate mean m1,m2 with items in k1 ={2,3,4,10,11,12}  and k2= {20,25,30}

Therfore m1 =(2+3+4+10+11+12)/6  =  7                                                                                                                                                    m2 =(11+12+20+25+30)/3 = 25

Now we have DistanceMean1 (7) ,DistanceMean2 (25) 

M1	M2	K1	K2
2	4	{2,3}	{4,10,11,12,20,25,30}
2.5	16	{2,3,4}	{10,11,12,20,25,30}
3	18	{2,3,4,10}	{11,12,20,25,30}
4.75	19.6	{2,3,4,10,11,12}	{20,25,30}
7	25	{2,3,4,10,11,12}	{20,25,30}

Recalculate mean m1,m2 with items in k1 ={2,3,4,10,11,12}  and k2= {20,25,30}

Therfore m1 =(2+3+4+10+11+12)/6  =  7                                                                                                                                                    m2 =(11+12+20+25+30)/3 = 25

Now we have DistanceMean1 (7) ,DistanceMean2 (25) 

Since we have same mean as previous iteration we stop here.

Thus  k1 = {2,3,4,10,11,12} and k2 = {20,25,30}