Clustering Methods K- means. K-means Algorithm Assume that K=3 and initially the points are assigned to clusters as follows. C 1 ={x 1,x 2,x 3 }, C 2.

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Presentation transcript:

Clustering Methods K- means

K-means Algorithm

Assume that K=3 and initially the points are assigned to clusters as follows. C 1 ={x 1,x 2,x 3 }, C 2 ={x 4,x 5,x 6 } and C 3 ={x 7,x 8 }. Apply the K-means algorithm until convergence.(i.e. untill the clusters do not change), using the manhattan distance. Problem Statement

Given data X1=(1,9) X2=(1,2) X3=(9,5) X4=(4,7) X5=(10,6) X6=(7,5) X7=(2,3) X8=(4,8)

K-means  The initial centroids are  C 1 ={x 1,x 2,x 3 }  C 2 ={x 4,x 5,x 6 }  C 3 ={x 7,x 8 }

K-means Manhattan distance Distance calculation:

Iteration 1 The table shows the distance between the object and centroids

Iteration 1 New centroids

Iteration 2 The table shows the distance between the object and new centroids

Iteration 2 New centroids

Interation 3 The table shows the distance between the object and new centroids

Iteration 3 New centroids

Results At this stage centroid remains same. The K-means algorithm converges here. Thus the final centroids are ◦ C 1 =(3,8) ◦ C 2 =(8.67,5.33) ◦ C 3 =(1.5,2.5)

Results