Solution

The correct answer is (D), (A), (B), (C), (E) 

EXPLANATION:

• Specify the number of clusters (K) to partition the data into (D).
  • The first step in K-means clustering is deciding how many clusters you want to end up with. This is typically determined based on your understanding of the data and the specific objectives of your analysis.
• Randomly initialize cluster centroids (A).
  • ​After deciding on the number of clusters, initialize their centers or "centroids". This is often done randomly, though there are various strategies for choosing initial centroids.
• Assign each data point to the nearest cluster centroid (B).
  • This step involves measuring the distance between each data point and each of the centroids, and then assigning each data point to the nearest one. The distance is usually calculated using a method like the Euclidean distance.
• Update the cluster centroids based on the mean of data points assigned to each cluster (C).
  • Once all data points have been assigned to clusters, we can re-calculate the center of each cluster. This is generally done by taking the mean of all the data points currently assigned to the cluster.
• Repeat steps B and C until convergence criteria are met (E).
  • The process of assigning data points to clusters and updating the centroids is repeated multiple times. Each repetition refines the cluster assignments and centroids. The algorithm continues to iterate until a stopping condition or convergence criteria is met. This could be a fixed number of iterations, or stopping when the change in centroids falls below a set threshold (i.e., the centroids have stabilized).

So in summary, we start by deciding on the number of clusters, initialize their centers, assign data points to the nearest centers, and then keep updating the centers and re-assigning data points until the centers stop moving significantly. This is how K-means clustering works.