I have gotten the following question as a test question for my exam and I simply cannot understand the answer.
A scatter plot of the data projected onto the first two principal components is shown below. We wish to examine if there exists some group structure in the data set. To do this, we have run the k-means algorithm with k = 2 using the Euclidean distance measure. The result of the k-means algorithm can vary between runs depending on the random initial conditions. We ran the algorithm several times and got some different clustering results.
Only three of the four clusterings shown can be obtained by running the k-means algorithm on the data. Which one can not be obtained by k-means? (there's nothing special about the data)
The correct answer is D. Can any of you explain why?