Question

Which of the following BEST describes why it is advised to run the - means clustering algorithm several times with different initial centroids?

A. The objective function is not convex

B. The algorithm is likely to suffer numerical overflows, hence the re-runs

C. Each successive run will yield better performance

D. The number of clusters might be different for each run.

E. None of the above

Answer 1

The -means clustering algorithm is an iterative algorithm that partitions data into k clusters. Running the algorithm several times with different initial centroids helps to find the best clustering solution. The number of clusters might be different for each run.

Step-by-step explanation:

The -means clustering algorithm is an iterative algorithm that partitions data into k clusters, where k is predetermined. The algorithm starts with randomly selected initial centroids and assigns each data point to the nearest centroid. After that, it computes new centroids based on the data points assigned to each cluster and repeats the process until the centroids stabilize.

It is advised to run the algorithm several times with different initial centroids because the objective function is not convex. This means that different starting points may lead to different clustering results. Running the algorithm multiple times helps to find the best clustering solution and reduces the impact of any initial centroid selection bias.

Therefore, the correct answer is D. The number of clusters might be different for each run as the algorithm explores different possible clustering outcomes with different initial centroids.