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(Solved): Question 3 Let x={x_(1),x_(2),x_(3),x_(4),x_(5),x_(6),x_(7),x_(8)} be a set of data points given by ...
Question 3
Let x={x_(1),x_(2),x_(3),x_(4),x_(5),x_(6),x_(7),x_(8)} be a set of data points given by
x_(1)=[[1],[3],[-2]]
x_(2)=[[4],[-1],[6]]
x_(3)=[[-1],[2],[0]]
x_(4)=[[2],[5],[-2]]
x_(5)=[[4],[-1],[2]]
x_(6)=[[-1],[4],[-1]]
x_(7)=[[-2],[3],[1]]
x_(8)=[[1],[5],[-4]]
and let C^(0)={c_(1)^(0),c_(2)^(0)} be initial estimates of centroids, where
c_(1)^(0)=[[1],[1],[1]] and c_(2)^(0)=[[2],[2],[2]]
Questions:
Calculate the distortion Dist(C^(0),x) for the original centroids C^(0) relative to x using the
Euclidean metric d_(2).Calculate the new values c_(1)^(1) and c_(2)^(1) of c_(1)^(0) and c_(2)^(0), respectively, after one iteration of k -
means clustering using the Euclidean d_(2) metric.
Calculate the distortion Dist(C^(1),x) for the new centroids C^(1) relative to x using the Eu-
clidea d_(2) metric.
Calculate the new values of c_(1)^(1) and c_(2)^(1) of c_(1)^(0) and c_(2)^(0), respectively, after one iteration of
k-means clustering using the "city block" d_(1) metric.