Question 4

A colleague has provided the following data containing four objects:

and the partially completed distance matrix of the four objects:

(a) Which metric was used to compute the distances?

(b) Compute the missing distance (marked “NA”).

(c) Your colleague wants to use k-means clustering on the four objects to obtain two clusters.

Explain why k-means should not be applied directly the the four objects, and how to transform the data into an appropriate form for k-means clustering.

(d) After transforming the data, we have obtained the four points below:

Your colleague wants to initialise the two k-means cluster centres to c1 = [8, 8] and c2 = [12, 12]. Which objects do you predict will belong to each cluster c1 and c2 after performing the k-means clustering?