Three data points are given in a 5-dimensional vector space.

A = [ 0 3 4 0 4]

B = [ 3 2 3 3 3]

C= [1 3 0 0 0]

a) Calculate the binary distance among the three pairs of data points.

b) Using single linkage clustering, write the order in which the three data points form two clusters using binary distance.

c) Multidimensional scaling has been used to reduce the data from 5 dimensions to 1. The 1-D vectors corresponding to A, B and C are as follows: A= [0.3] B= [0.1] C= [0.4] Assume two k-means cluster centres are initialized as c1=[0.2] and c2=[0.5].

Which object do you predict will belong to each cluster after performing k-means clustering (where c1 is the centre of cluster 1 and c2 is the centre of cluster 2) after one iteration of the clustering algorithm?

Points in Cluster 1: ___

Points in Cluster 2:_____

d) After assigning points to clusters in part (c), you recompute the new cluster centres of the points currently assigned to each cluster. For each cluster, write these new cluster centres.

Cluster 1 new centre: _________________ Cluster 2 new centre: _________________