means-hierarchical.pdf Adobe Acrobat Reader DC dow Help Assign2-Clustering The-Morgan-Kauf- abhi 3/4 100% 3. Either: Prove that k-means will produce k clusters, all nonempty, or: Give an example of a set D of data points (with no repeated data point), a value for k (ks-n, where n is the number of data objects), and a set of k data points as initial seeds, such that some cluster becomes empty, (30 pts) A motivation for this problem Many or most of you will become professional programmers. The programs you write are supposed to work all the time, not just 999 times out of 1000. The pseudocode for k-means in the textbook will fail if indeed one of the clusters becomes empty Question: is it safe to write the code for k-means as the textbook, or will code written like that get you into some trouble with your manager (not initially, but after a while)? If you decide to try to find a malevolent data you can try the following. Try a data file of 6 to 12 data points in the plane so that when k-means is performed to k = 3 or k = 4 clusters, in iteration 2 (or iteration 3 or ), one of the clusters becomes empty. The initial seeds must be data points: and your example should not rely on ties to accomplish its goals. (Comment this effort might be easier if you let most of the points be colinear.) 145 AM